1 Introduction

In many estuaries, the joint action of tidal currents and residual (time-mean) currents causes entrainment, transport, and settling of fine sediments. The resulting along-channel distribution of mean suspended sediment concentration (SSC) is often characterized by a turbidity maximum, i.e., a location where the concentration of suspended sediment attains a maximum, hence where the suspended sediment is trapped. Thus, a zone of sediment accumulation may form, causing navigational problems that consequently require dredging, as well as ecological problems, such as oxygen deficits (cf. Cloern and Jassby 2012, and references herein).

Such a situation actually occurs in the Yangtze Estuary, located at the east coast of mainland China. Here, a large-scale mouth-bar area is present (Fig. 1). One of four channels that intersect this bar is the North Passage, which has minimum depths that are less than 6.5 m in the main channel. To improve navigability of the major channel toward Shanghai Harbor, a large-scale Deep Waterway Project (DWP) was carried out during the period 1998 until 2011. The main engineering works included two wide spacing training walls, 19 long groins, diversion works, and jetties. These constructions were completed in 2004, while after that, the deepening of the waterway relied on local lengthening of groins and dredging. The waterway was deepened to 8.5 m (June 2001), 10 m (March 2005), and finally to 12.5 m (May 2011). To maintain the water depth, the annual dredging rates were around 20, 40, and 70 million tons, respectively. The quantity of dredging was significantly larger than 25 million tons per year that engineers originally anticipated. Since the third phase of the project started, the dredging has taken place continuously and caused a persistent background SSC. The along-channel distribution of the siltation corresponded to the distribution of suspended sediment, and most siltation occurred in the core area of turbidity maximum (Shanghai Waterway Engineering Design and Consulting Co., Ltd. 2011). Thus, clear understanding of mechanisms that affect along-channel residual sediment transport and its response to the interventions is required to help decreasing siltation in the waterway and to improve decision strategies for estuarine management.

Fig. 1
figure 1

Map of the lower Yangtze Estuary. The red solid lines indicate the training walls, groins, and jetties constructed in the Deep Waterway Project

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Along-channel residual sediment transport in tidal estuaries is mainly driven by residual currents, tidal asymmetries, and sediment processes associated with the settling, erosion, and flocculation of sediment (Officer 1981; Dyer 1997; Winterwerp 2002). Residual flows in the along-channel direction can be generated by river discharge, horizontal density gradients due to salinity and turbidity gradients (Hansen and Rattray 1965; Festa and Hansen 1978; Talke et al. 2009), wind drag on the sea surface (North et al. 2004), tidal rectification (Huijts et al. 2009), and by asymmetries in stratification and mixing (Stacey et al. 2008; Burchard and Hetland 2010; Cheng et al. 2011). Besides residual sediment transport due to residual currents, tidal pumping mechanisms related to correlations between tidal currents and SSC were considered to be significant in sediment trapping (Dyer 1997; Li and Zhang 1998). Tidal pumping mechanisms investigated include transport by spatial settling lag (Postma 1967) and by combined tidal asymmetry and settling lag (Groen 1967; Jay and Musiak 1994; Schuttelaars and de Swart 1996; Chernetsky et al. 2010).

Dyer (1988, 1997) introduced a method to decompose observed residual sediment transport into several terms, involving transport by Eulerian residual flow, Stokes transport, and tidal pumping. This method has been applied to several estuaries to identify mechanisms causing net sediment transport (Dyer 1988; Uncles et al. 1984, 1985). It was also applied to the Yangtze Estuary by Li and Zhang (1998) using field data surveyed in 1988. They showed that net sediment transport in the North Passage was mainly dominated by a seaward contribution due to residual flow and two landward contributions due to tidal pumping and Stokes transport. Liu et al. (2011) identified the importance of the landward residual flow in the bottom layer in sediment trapping by analyzing data surveyed in a dry season in the end phase of the DWP (January 2008). However, no identification of the roles of different tidal components was presented, nor that of residual flows forced by different agents. Besides, variation in the mechanisms of along-channel sediment transport prior to and after the interventions in the North Passage is still an open problem.

The purpose of this paper is to identify the effects of the DWP (engineering works and the continuous maintenance dredging) on the flow structure, suspended sediment distribution, and its net transport (i.e., tidal averaged transport) along the main channel of the North Passage, with focus on explaining the changes in net sediment transport in terms of physical mechanisms. A new approach, based on combining harmonic analysis of field data and theoretical results of an analytical model, will be used to assess flow and net sediment transport due to individual mechanisms. In Section 2, the details on the field measurements are presented, followed by a description of the method of harmonic analysis on water height, velocity, and SSC data, as well as computation of net sediment fluxes and transports due to individual harmonic components. Also, the analytical model to derive the main residual flow components is presented here. In Section 3, the results of tidal and seasonal variation of SSC prior to and after DWP are presented, focusing on the changes in the strength and location of the ETM. This is followed by showing the harmonic components of the flow and SSC and the net sediment fluxes, as well as transports that they induce. Also, the physical mechanisms that underlie these transports will be identified. Section 4 contains a discussion and the last section contains the conclusions.

2 Data and methods

2.1 Data

Measurements were carried out simultaneously at several stations in the main channel of the North Passage (Fig. 2) by anchoring a boat at each station. Due to the fact that it is forbidden to perform long-term measurements in the waterway, all the measurement sites were just outside the deep waterway (Fig. 2), either slightly to the north or to the south. Selection of the sites was based on the criterion that here the strongest tidal current in the cross section, excluding the waterway, occurs.

Fig. 2
figure 2

Locations of the stations where data of flow, salinity, and suspended sediment concentration were collected during tidal cycles in the North Passage. The blue dotted lines are the boundaries of different reaches, and the definition of each reach is used for interpretation in the text. The dark blue circle is the reference point at the landward boundary of the North Passage

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These measurements, organized by Yangtze Estuary Waterway Administration Bureau, Ministry of Transport of China, were undertaken at spring tides during June 1999, February 2000, August 2008, and February 2009, under calm weather conditions. During these campaigns, data of along-channel currents, salinity, and SSC at difference depths were collected during one to two full tidal cycles. These data were collected at six locations with relative depths of 0 (actually 0.5 m below the water surface), 0.2, 0.4, 0.6, 0.8, and 1 (near bottom) of each station at every hour. The current velocity was measured by direct-reading current meters, and salinity and SSC were obtained by analyzing water samples taken during measurements. The direct-reading current meter is a device that was widely used prior to availability of ADCP (cf. Uncles et al. 2006). The current meter used in the measurements is type SLC9-2, a mechanical current meter with a propeller to measure the velocity of the current and a rudder at the end to control the current meter to be parallel to the direction of current, produced by the Instrument Company of Qingdao Ocean University (now China Ocean University), with an accuracy of 0.01 m s−1.

The detailed information about each survey measurement, involving the exact time, duration, stations, and monthly mean river discharge at the tidal limit, is presented in Table 1. The data of June 1999 and February 2000 were considered to represent the conditions prior to the interventions during the wet and dry season, and the data of August 2008 and February 2009 were considered to represent the conditions after the interventions during the wet and dry season. Hereafter, these four cases are called the wet season prior to the DWP, dry season prior to the DWP, wet season after the DWP, and dry season after the DWP. The difference in river discharge corresponding to the measurements of the same season in different years is 7 % in the wet season and 5 % in the dry season. Thus, the data prior to and after the interventions are comparable.

Table 1 Detailed information on survey measurements
Full size table

2.2 Harmonic analysis

To identify the net sediment transport due to different agents, it is convenient to decompose tidal height, velocity, and SSC into their mean components and components related to tides by harmonic analysis. According to the harmonic analysis on the long time tidal height series, the tide in the Yangtze Estuary is dominated by the diurnal tide (O 1, K 1), semi-diurnal tide (M 2), and quarter-diurnal tide (M 4), so these data are decomposed into a mean part and three tidal components. Due to the fact that the differences between tidal frequencies of O 1 and K 1 are small, these two tidal constituents are not separated in the harmonic analysis, and they are represented by a diurnal tidal component with a frequency of 0.7 × 10−4 s−1.

The tidal height data for a given period of time at a certain station is thus represented as a harmonic series

$$ h(t)=H+{\eta_1}\cos \left( {{\sigma_1}t-{\psi_1}} \right)+{\eta_2}\cos \left( {{\sigma_2}t-{\psi_2}} \right)+{\eta_3}\cos \left( {{\sigma_3}t-{\psi_3}} \right) $$
(1)

Here, h is the measured instantaneous water depth and t is time. Further, H is the mean water depth, and σ 1 ∼ 0.7 × 10−4 s−1, σ 2 ∼ 1.4 × 10−4 s−1, and σ 3 ∼ 2.8 × 10−4 s−1 are the tidal frequencies of the diurnal tide, semi-diurnal tide, and quarter-diurnal tide. Furthermore, η 1, η 2, η 3, and Ψ 1, Ψ 2, Ψ 3 are the amplitudes and phases of diurnal tidal constituent O 1–K 1, semi-diurnal tidal constituent M 2, and quarter-diurnal tidal constituent M 4. The values of these coefficients are determined by minimizing the overall error between observed and modeled h(t).

Data of velocity and SSC at one station are used at six locations with relative depth of 0, 0.2, 0.4, 0.6, 0.8, and 1 at every hour. Thus, flow velocity is decomposed as

$$ u\left( {t,j} \right)={U_0}(j)+{U_1}(j)\cos \left( {{\sigma_1}t-{\varphi_1}(j)} \right)+{U_2}(j)\cos \left( {{\sigma_2}t-{\varphi_2}(j)} \right)+{U_3}(j)\cos \left( {{\sigma_3}t-{\varphi_3}(j)} \right) $$
(2)

Here, j denotes the vertical location of the measurements, equaling 1 to 6 from surface to bottom. Further, u is the measured velocity, U 0 is the residual flow, while U 1, U 2, U 3 and φ 1, φ 2, φ 3 are the amplitudes and phases of diurnal tidal current, semi-diurnal tidal current, and quarter-diurnal tidal current.

Suspended sediment concentration is decomposed as

$$ c\left( {t,j} \right)={C_0}(j)+{C_1}(j)\cos \left( {{\sigma_1}t-{\theta_1}(j)} \right)+{C_2}(j)\cos \left( {{\sigma_2}t-{\theta_2}(j)} \right)+{C_3}(j)\cos \left( {{\sigma_3}t-{\theta_3}(j)} \right) $$
(3)

In this expression, c is the measured SSC and C 0 is the tidal averaged concentration, which includes the contribution from sediment input from the river and sediment resuspension due to residual flow, tide, wave action, and dredging. Furthermore, C 1, C 2, C 3 and θ 1, θ 2, θ 3 are the amplitudes and phases of concentration related to diurnal tide, semi-diurnal tide, and quarter-diurnal tide, respectively.

Next, the local net sediment flux F(j) due to residual flow and various tidal pumping mechanisms is considered. From Eqs. 2 and 3, it follows

$$ \begin{array}{*{20}c} {F(j)=\overline{{u\left( {j,t} \right)c\left( {j,t} \right)}}} \hfill & {=\underbrace{{{U_0}(j){C_0}(j)}}_{{{F_0}}}+\underbrace{{{U_1}(j){C_1}(j)\cos \left( {{\varphi_1}(j)-{\theta_1}(j)} \right)/2}}_{{{F_{{\mathrm{O}1,\mathrm{K}1}}}}}} \hfill \\ {} \hfill & {+\underbrace{{{U_2}(j){C_2}(j)\cos \left( {{\varphi_2}(j)-{\theta_2}(j)} \right)/2}}_{{{F_{{\mathrm{M}2}}}}}+\underbrace{{{U_3}(j){C_3}(j)\cos \left( {{\varphi_3}(j)-{\theta_3}(j)} \right)/2}}_{{{F_{{\mathrm{M}4}}}}}} \hfill \\ \end{array} $$
(4)

Here, the overbar \( \overline{\bullet} \) denotes averaging over a tidal period, F 0 is the net sediment flux due to residual flow, and F O1,K1, F M2, F M4 are net fluxes related to the diurnal tide O 1–K 1, semi-diurnal tide M 2, and quarter-diurnal tide M 4. Longitudinal–vertical structure of net sediment flux due to individual forcing agents was obtained by interpolating sediment fluxes at different locations. The spatial interpolation was done in Matlab with a cubic spline interpolation method. Additional analysis of the August 2008 data was performed, in which we used a different interpolation scheme (cubic). The relative error between these data was found them to be small (less than 1 %).

Finally, the net sediment transport per unit width was computed, which is the tidal average of the vertical integration of the sediment flux. Due to the fact that data are available at only six locations of a vertical water column, it is assumed that the water column can be divided into six layers and the observed velocity and SSC at a certain relative depth represent the average condition of the layer in which it locates. So, the net sediment transport per unit width is the discrete integration of the sediment fluxes at the six relative depths:

$$ \begin{array}{*{20}c} {T=\mathop{\sum}\limits_{j=1}^6\overline{{u\left( {j,t} \right)c\left( {j,t} \right)h(t)p(j)}}} \hfill & {=\underbrace{{\mathop{\sum}\limits_{j=1}^6{F_0}(j)p(j)H}}_{{{T_0}}}} \hfill \\ {} \hfill & {+\underbrace{{\mathop{\sum}\limits_{j=1}^6{F_{O1,K1 }}(j)p(j)H}}_{{{T_{O1,K1 }}}}+\underbrace{{\mathop{\sum}\limits_{j=1}^6{F_{M2 }}(j)p(j)H}}_{{{T_{M2 }}}}+\underbrace{{\mathop{\sum}\limits_{j=1}^6{F_{M4 }}(j)p(j)H}}_{{{T_{M4 }}}}} \hfill \\ {} \hfill & {+\underbrace{{\mathop{\sum}\limits_{i=1}^3\mathop{\sum}\limits_{j=1}^6{U_i}(j){\eta_i}(j)\cos \left( {{\varphi_i}(j)-{\psi_i}(j)} \right){C_0}(j)p(j)/2}}_{{{T_{{\eta u{C_0}}}}}}} \hfill \\ {} \hfill & {+\underbrace{{\mathop{\sum}\limits_{i=1}^3\mathop{\sum}\limits_{j=1}^6{C_i}(j){\eta_i}(j)\ \cos\ \left( {{\theta_i}(j)-{\psi_i}(j)} \right){U_0}(j)p(j)/2}}_{{{T_{{\eta c{U_0}}}}}}+{T_{{\eta cu}}},} \hfill \\ \end{array} $$
(5)

where

$$ \begin{array}{*{20}c} {{T_{{\eta cu}}}} \hfill & {=\mathop{\sum}\limits_{j=1}^6{U_1}(j){\eta_2}(j){C_1}(j)\cos \left( {{\varphi_1}(j)-{\psi_2}(j)+{\theta_1}(j)} \right)p(j)/4} \hfill \\ {} \hfill & {+\mathop{\sum}\limits_{j=1}^6{U_2}(j){\eta_1}(j){C_1}(j)\cos \left( {{\varphi_2}(j)-{\psi_1}(j)-{\theta_1}(j)} \right)p(j)/4} \hfill \\ {} \hfill & {+\mathop{\sum}\limits_{j=1}^6{U_1}(j){\eta_1}(j){C_2}(j)\cos \left( {{\varphi_1}(j)+{\psi_1}(j)-{\theta_2}(j)} \right)p(j)/4} \hfill \\ {} \hfill & {+\mathop{\sum}\limits_{j=1}^6{U_3}(j){\eta_2}(j){C_2}(j)\cos \left( {{\varphi_3}(j)-{\psi_2}(j)-{\theta_2}(j)} \right)p(j)/4} \hfill \\ {} \hfill & {+\mathop{\sum}\limits_{j=1}^6{U_2}(j){\eta_2}(j){C_3}(j)\cos \left( {{\varphi_2}(j)+{\psi_2}(j)-{\theta_3}(j)} \right)p(j)/4} \hfill \\ \end{array} $$

Here, the upper bar denotes a tidal-average or mean. Further, j denotes layers, and p(j) is the relative thickness of the layer, which is 0.1, 0.2, 0.2, 0.2, 0.2, and 0.1 from surface to bottom. Furthermore, T 0 is the net sediment transport due to residual flow, and T O1,K1, T M2, T M4 are net transports related to O 1–K 1, M 2, and M 4 tidal pumping mechanisms, respectively. Component \( {T_{{\eta u{C_0}}}} \) is the net sediment transport due to the correlation between the sea level variation and the tidal current, acting with mean SSC. Component \( {T_{{\eta c{U_0}}}} \) is the net sediment transport due to the correlation between the tidal components of sea level variation and SSC, acting with the residual flow. Finally, \( {T_{{\eta cu}}} \) is the net sediment transport due to the triple correlation of tidal components of sea level variation, velocity, and SSC.

Due to the fact that the measurement for June 1999 only lasted for 14 h, a test was done to investigate how accurate the O 1–K 1 components are obtained from the 14 h. To address this point, we took the August 2008 data (which spans 25 h) and remained only the first 14 h. From this, new data set values of the O 1–K 1 components were computed. The results showed that the difference between this new data set (14 h) and the original data set (25 h) was around 20 %, which is considered to be acceptable in our study.

2.3 Deriving main components of residual flow

In order to identify the net sediment transport due to different residual flow components, a simple analytical model was used to derive residual flow components that are forced by individual physical mechanisms, involving river discharge, density-driven flow, Stokes return flow, tidal rectification, and asymmetry in mixing during the tidal cycle. The model resembles that used by Ianiello (1977), McCarthy (1993), and Cheng et al. (2010), but the bottom boundary condition is modified from no slip to partial slip. The difference with the model of Chernetsky et al. (2010) is that open boundary is used at the seaward and landward sides. The model assumptions and equation-solving techniques follow previous models. The model domain is a straight estuary channel that has constant depth and width, with cross-channel uniform conditions (Fig. 3).

Fig. 3
figure 3

Sketch of the model geometry. The blue dashed lines represent tidal elevations. Location x = 0 corresponds to that of the reference point in Fig. 2

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In contrast to more sophisticated numerical models, the present model only yields an approximate description of the complex geometry and dynamics of the North Passage. Yet, it has a major advantage, viz. that it allows for systematic assessment of the contribution of residual flow components generated by different forcing agents to the total net sediment flux and net sediment transport. In this way, more fundamental insight into the complex dynamics of the system is obtained. The success of earlier models of this kind, which were cited above, motivates the application of this approach.

2.3.1 Governing equations

The flow in the along-channel direction is governed by the shallow water equation for cross-channel uniform conditions,

$$ \frac{{\partial u}}{{\partial t}}+u\frac{{\partial u}}{{\partial x}}+w\frac{{\partial u}}{{\partial z}}=-g\frac{{\partial \eta }}{{\partial x}}+\frac{g}{{{\rho_0}}}\frac{{d\rho }}{dx }z+\frac{\partial }{{\partial z}}\left( {A\frac{{\partial u}}{{\partial z}}} \right), $$
(6a)
$$ \frac{{\partial u}}{{\partial x}}+\frac{{\partial w}}{{\partial z}}=0. $$
(6b)

Here, x (u) and z (w) denote the along-channel and vertical coordinates (velocity components), g is gravitational acceleration, and ρ 0 ∼ 1,020 kg m−3 is the reference density. The along-channel density gradient is prescribed and denoted by dρ/dx. Furthermore, η is the location of the free surface, and A is the vertical eddy viscosity coefficient, which varies during the tidal cycle. Following Cheng et al. (2010), as a result of tidal straining, the vertical eddy viscosity coefficient can be written as

$$ A=\overline{A}+{A_1}\cos \left( {{\sigma_2}t-\alpha } \right), $$
(7)

where

$$ {A_1}=\overline{A}\left| {\frac{{\operatorname{d}\rho }}{{\operatorname{d}x}}} \right|\left( {\frac{U}{{{\sigma_2}\varDelta \rho }}} \right). $$

Here, \( \bar{A} \) is a constant, tidal mean eddy viscosity coefficient. Further, \( {{A}_{1}}( < \bar{A}) \)is the amplitude of the tidal varying part which depends on the horizontal density gradient and tidal flow amplitude, where Δρ is the typical density difference and U is the typical tidal velocity. Physically, A 1 is proportional to the tidal mean eddy viscosity coefficient \( \left( {\overline{A}} \right) \), density gradient over typical density difference (|dρ/dx|/Δρ), and the typical length scale over which density gradient is advected (U/σ 2). Furthermore, α is a phase. Following Simpson et al. (1990) and Stacey et al. (2008), the strongest A occurs at the end of flood.

At the surface, it is assumed that the water motion is stress free and satisfies the kinematic boundary condition,

$$ A\frac{{\partial u}}{{\partial z}}=0,w=\frac{{\operatorname{d}\eta }}{{\operatorname{d}t}},\mathrm{at}\ z=\eta . $$
(8a)

At the bottom, a partial slip condition and impermeability of the bottom are imposed,

$$ A\frac{{\partial u}}{{\partial z}}=su,w=0,\mathrm{at}\ z=-H. $$
(8b)

At the landward boundary, a net transport of water due to freshwater input (q, discharge per time per unit width) is imposed. Integration of continuity Eq. 6b and application of boundary conditions (Eqs. 8a, 8b, 8c, 8d, and 8e) then imply constant residual water transport along the channel,

$$ \overline{{\mathop{\smallint}\limits_{-H}^{\eta }u \operatorname {d}z}}=q,\ \ \mathrm{for}\ \mathrm{all}\ x. $$
(8c)

Here, the overbar \( \overline{\bullet} \) denotes a tidal average or mean.

Finally, semi-diurnal tidal sea level variations are imposed at both side boundaries with amplitude Z, frequency σ 2, and phase angle Ψ:

$$ {\eta_{M2 }}\left( {0,t} \right)={Z_0}\cos \left( {{\sigma_2}t-{\psi_0}} \right),\ \ \ \mathrm{at}\ x=0\left( {\mathrm{landward}\ \mathrm{boundary}} \right), $$
(8d)
$$ {\eta_{M2 }}\left( {L,t} \right)={Z_L}\cos \left( {{\sigma_2}t-{\psi_L}} \right),\ \ \ \mathrm{at}\ x=L\ \left( {\mathrm{seaward}\ \mathrm{boundary}} \right). $$
(8e)

2.3.2 Perturbation analysis and analytical results

By performing a perturbation analysis similar to, e.g., Ianiello (1977), a reduced and consistent set of model equations is obtained. Application of scaling analysis on the equation terms reveals a parameter ε, the tidal amplitude-to-depth ratio, which measures the intensity of the nonlinear terms with respect to that of linear terms. It is assumed that the parameter ε is not negligible but much smaller than 1. By collecting terms with equal powers of ε, a leading order system of equations (ε 0 terms) and a first-order system of equations (ε 1 terms) are obtained. Higher-order systems are not considered.

The leading order system of equations governs the semi-diurnal tidal motion, and the equations are given by

$$ \frac{{\partial {u_0}}}{{\partial t}}=-g\frac{{\partial {\eta_0}}}{{\partial x}} + \overline{A}\frac{{{\partial^2}{u_0}}}{{\partial {z^2}}}, $$
(9a)
$$ \frac{{\partial {u_0}}}{{\partial x}}+\frac{{\partial {w_0}}}{{\partial z}}=0, $$
(9b)

where the subscript 0 represents leading order.

The boundary conditions at the free surface and at the bottom are given by

$$ \frac{{\partial {u_0}}}{{\partial z}}=0,\ \ {w_0}=\frac{{\operatorname{d}{\eta_0}}}{{\operatorname{d}t}},\mathrm{at}\ z=0, $$
(10a)
$$ \overline{A}\frac{{\partial {u_0}}}{{\partial z}}=s{u_0},\ \ {w_0}=0,\ \ \mathrm{at}\ z=-H. $$
(10b)

At the side boundaries, the system was forced by externally prescribed semi-diurnal tides

$$ {\eta_0}\left( {0,t} \right)={Z_0}\cos \left( {{\sigma_2}t-{\psi_0}} \right),\ \ \ \mathrm{at}\ x=0\ \left( {\mathrm{landward}\ \mathrm{boundary}} \right), $$
(10c)
$$ {\eta_0}\left( {L,t} \right)={Z_L}\cos \left( {{\sigma_2}t-{\psi_L}} \right),\ \ \ \mathrm{at}\ x=L\left( {\mathrm{seaward}\ \mathrm{boundary}} \right). $$
(10d)

Analytical solutions for the tidal motion (Eqs. 9a, 9b, 10a, 10b, 10c, and 10d) are

$$ {\eta_0}=Re\left\{ {\widehat{\eta}(x){e^{{-i{\sigma_2}t}}}} \right\}, $$
(11)
$$ {u_0}=Re\left\{ {\widehat{u}(x,z){e^{{-i{\sigma_2}t}}}} \right\}, $$
(12)

where Re denotes the real part of a complex variable, and

$$ \widehat{\eta}=\frac{{{Z_0}{e^{{i{\psi_0}}}}\ \sin \left[ {{k_{*}}\left( {L-x} \right)} \right]+{Z_L}{e^{{i{\psi_L}}}}\ \sin \left( {{k_{*}}x} \right)}}{{\sin \left( {{k_{*}}L} \right)}},\widehat{u}=\frac{ig }{{{\sigma_2}}}\frac{{d\widehat{\eta}}}{dx}\left[ {\frac{{\cosh (\mu z)}}{{\cosh \left( {\mu H} \right)+\frac{\mu }{s}\sinh (\mu H)}}-1} \right], $$

with

$$ \frac{{d\widehat{\eta}}}{dx }=-{k_{*}}\frac{{{Z_0}{e^{{i{\psi_0}}}}\ \cos \left[ {{k_{*}}\left( {L-x} \right)} \right]+{Z_L}{e^{{i{\psi_L}}}}\ \cos ({k_{*}}x)}}{{\sin ({k_{*}}L)}},\mu =\sqrt{{\frac{{\ {\sigma_2}}}{{2\overline{A}}}}}\left( {1-i} \right),{k_{*}}=\frac{{{\sigma_2}}}{{\sqrt{gH }}}{{\left[ {1-\frac{{\tanh \left( {\mu H} \right)}}{{\mu H}}\frac{s}{{s+\mu \tanh (\mu H)}}} \right]}^{{-\frac{1}{2}}}}. $$

The system governing the dynamics of the dominant part of the residual flow is obtained by considering the first-order system (which contains terms that are an order ε smaller than the dominant tidal terms) and averaging these equations over a tidal cycle. This procedure, which is discussed in detail by Ianiello (1977) and Cheng et al. (2010), results in

$$ \underbrace{{\overline{{{u_0}\frac{{\partial {u_0}}}{{\partial x}}}}+\overline{{{w_0}\frac{{\partial {u_0}}}{{\partial z}}}}}}_t=-g\overline{{\frac{{\operatorname{d}{\eta_1}}}{{\operatorname{d}x}}}}+\underbrace{{\frac{g}{\rho}\frac{{\operatorname{d}\rho }}{{\operatorname{d}x}}z}}_d+\overline{A}\overline{{\frac{{{\partial^2}{u_1}}}{{\partial {z^2}}}}}+\underbrace{{\overline{{{A_{{1\,}}}\cos ({\sigma_2}t-\alpha )\frac{{{\partial^2}{u_0}}}{{\partial {z^2}}}}}}}_a, $$
(13a)
$$ \mathop{\smallint}\limits_{-H}^0\overline{{{u_1}}} \operatorname {d}z+\underbrace{{\overline{{{\eta_0}{{{\left. {{u_0}} \right|}}_{z=0}}}}}}_s=\underbrace{q}_q. $$
(13b)

In these expressions, the overbar \( \overline{\bullet} \) denotes averaging over a tidal period. Besides, q is the freshwater discharge per unit width and subscript 1 represent first order. Further, \( \underbrace{\bullet} \) denotes the individual forcing terms.

The boundary conditions at the free surface and at the bottom are given by

$$ \frac{{\partial {u_1}}}{{\partial z}}+\underbrace{{\overline{{{\eta_0}\frac{{{\partial^2}{u_0}}}{{\partial {z^2}}}}}}}_b=0,\ \ \ \ \mathrm{at}\ z=0, $$
(14a)
$$ \overline{A}\frac{{\partial {u_1}}}{{\partial z}}=s{u_1},\ \ \mathrm{at}\ z=-H. $$
(14b)

Eqs. 13a and 13b together with boundary conditions 14a and 14b describe the residual water motion in the estuary which is driven by the residual forcing terms that are river discharge (q), along-channel density gradient (d), Stokes return water transport which compensates for the Stokes drift, i.e., correlation between horizontal and vertical water motion (s), stress-free surface condition (b), nonlinear tidal momentum advection (t), and asymmetric tidal mixing (a). Since the equations are linear, the residual flow due to each forcing mechanism can be derived separately, i.e., the resulting solution for the along-channel residual flow u 1 and the sea surface elevation η 1 reads

$$ {\chi_1}={\chi_d}+{\chi_q}+{\chi_s}+{\chi_b}+{\chi_t}+{\chi_a}, $$
(15)

where \( {\chi_1}=\left( {{u_1},{\eta_1}} \right). \)

The analytical solution for the residual flow components are

$$ {u_d}=-\frac{g}{{48\overline{A}}}\frac{1}{\rho}\frac{{\operatorname{d}\rho }}{{\operatorname{d}x}}\left[ {9\left( {{z^2}-{H^2}-\frac{{2\overline{A}H}}{s}} \right)\left( {\frac{{4\overline{A}H+s{H^2}}}{{3\overline{A}+sH}}} \right)+8\left( {{z^3}-{H^3}-\frac{{3\overline{A}{H^2}}}{s}} \right)} \right], $$
(16)
$$ {u_q}=-\frac{q}{{\frac{{{H^3}}}{3}+\frac{{\overline{A}{H^2}}}{s}}}\left( {\frac{{{z^2}-{H^2}}}{2}-\frac{{\overline{A}H}}{s}} \right), $$
(17)
$$ {u_s}=\frac{{\overline{{{\eta_0}{{{\left. {{u_0}} \right|}}_{z=0 }}}}}}{{\frac{{{H^3}}}{3}+\frac{{\overline{A}{H^2}}}{s}}}\left( {\frac{{{z^2}-{H^2}}}{2}-\frac{{\overline{A}H}}{s}} \right), $$
(18)
$$ {u_b}=-\overline{{{\eta_0}{{{\left. {\frac{{{\partial^2}{u_0}}}{{\partial {z^2}}}} \right|}}_{z=0 }}}}\left[ {\frac{3}{4H}\left( {\frac{{2\overline{A}+sH}}{{3\overline{A}+sH}}} \right)\left( {{z^2}-{H^2}-\frac{{2\overline{A}H}}{s}} \right)+\left( {z+H+\frac{\overline{A}}{s}} \right)} \right] $$
(19)
$$ {u_t}=\left( {\frac{{\frac{{{z^2}-{H^2}}}{{2\overline{A}}}-\frac{H}{s}}}{{\frac{{{H^3}}}{{3\overline{A}}}+\frac{{{H^2}}}{s}}}} \right)\left( {\frac{1}{\overline{A}}\mathop{\smallint}\limits_{-H}^0I\left( {{F_t}} \right)\operatorname{d}z+\frac{H}{s}\mathop{\smallint}\limits_0^{-H }{F_t}\left( {x,z} \right)\operatorname{d}z} \right)+\frac{{I\left( {{F_t}} \right)}}{\overline{A}}+\frac{{\mathop{\smallint}\nolimits_0^{-H }{F_t}\left( {x,z} \right)\operatorname{d}z}}{s}, $$
(20)

where

$$ \mathrm{I}\left( {{F_t}} \right)=\mathop{\smallint}\limits_{-H}^z\mathop{\smallint}\limits_0^{{{z^{'}}}}{F_t}(x,{z}^{\prime\prime})\operatorname{d}{z}^{\prime\prime}\operatorname{d}{z}^{\prime},{F_t}\left( {x,z} \right)=\overline{{{u_0}\frac{{\partial {u_0}}}{{\partial x}}}}+\overline{{{w_0}\frac{{\partial {u_0}}}{{\partial z}}}}. $$

Finally,

$$ {u_a}=\left( {-\frac{\overline{A}}{{2{A_1}}}} \right)\left( {\left( {\frac{{\frac{{{z^2}-{H^2}}}{{2\overline{A}}}-\frac{H}{s}}}{{\frac{{{H^3}}}{{3\overline{A}}}+\frac{{{H^2}}}{s}}}} \right)Re\left\{ {\mathop{\smallint}\limits_{-H}^0\widehat{u} \operatorname {d}z\exp (-i\alpha )} \right\}+Re\left\{ {\widehat{u}\,\exp (-i\alpha )} \right\}} \right). $$
(21)

Here, salinity data are used to compute density gradient dρ/dx, which is necessary to calculate flow components u d in Eq. 16 and u a in Eq. 21.

2.3.3 Estimation of values of density gradient, eddy viscosity, and slip number

The density gradient dρ/dx in Eqs. 16 and 21 was computed from salinity data S, assuming that density depends on salinity only, i.e., ρ = ρ 0 + βS(x), where β ∼ 0.83 kg m−3psu−1 and S is the vertical mean salinity averaged over a tidal cycle in practical salinity unit. The values of tidal mean eddy viscosity \( \overline{A} \) and slip number s were obtained by minimizing the difference between the observed and modeled M 2 tide current governed by the leading order system.

From the result of harmonic analysis on the field data, the M 2 tidal current can be written as

$$ {U_{M2 }}\left( {x,z} \right)\cos \left( {{\sigma_2}t-\varphi } \right)={U_c}\cos \left( {{\sigma_2}t} \right)+{U_s}\sin \left( {{\sigma_2}t} \right), $$
(22)

with \( {U_c}={U_{M2 }}\cos \left( \varphi \right)\mathrm{and}\ {U_s}={U_{M2 }}\sin \left( \varphi \right). \)The modeled M 2 tidal current reads

$$ {u_0}=Re\left\{ {\widehat{u}\left( {x,z} \right){e^{{-i{\sigma_2}t}}}} \right\}=\left| {\widehat{u}} \right|\cos \left( {{\sigma_2}t-\varphi \prime} \right)={U_c}\prime\cos \left( {{\sigma_2}t} \right)+{U_s}\prime\sin \left( {{\sigma_2}t} \right), $$
(23)

with \( {U_c}\prime=\left| {\widehat{u}} \right|\cos \left( {\varphi \prime} \right),\ {U_s}\prime=\left| {\widehat{u}} \right|\sin \left( {\varphi \prime} \right)\mathrm{and}\ \varphi \prime=\arg \left( {\widehat{u}} \right). \)

Thus, the expression for the difference between the observed and modeled M 2 tidal current is

$$ G(\overline{A},\ s)=\mathop{\sum}\limits_{i=1}^n\mathop{\sum}\limits_{j=1}^m\left[ {{{{\left( {{U_c}\left( {i,j} \right)-{U_c}'\left( {i,j} \right)} \right)}}^2}+{{{\left( {{U_s}\left( {i,j} \right)-{U_s}'\left( {i,j} \right)} \right)}}^2}} \right], $$
(24)

with n being the number of stations and m ∼ 6 the number of layers. By minimizing G with respect to \( \overline{A} \) and s, the values of these parameters corresponding to the smallest difference are obtained. The relative error is also used to represent the performance of the model, which reads

$$ \mathrm{RE}=G/\mathop{\sum}\limits_{i=1}^n\mathop{\sum}\limits_{j=1}^m\left( {{U_c}{{{\left( {i,j} \right)}}^2}+{U_s}{{{\left( {i,j} \right)}}^2}} \right). $$
(25)

3 Results

3.1 Field data

3.1.1 Tidal and seasonal behavior of SSC

Figure 4 shows the vertical distribution of currents and SSC at station CS3 during a tidal cycle prior to and after the DWP. The left panels show distributions in the wet seasons while right panels show distributions in the dry seasons. In the electronic supplement, the velocity and SSC data over the full measurement period are shown for three representative stations, i.e., CS2, CS3, and CS4. Salinity data are not shown, as this study focuses on flow and SSC dynamics. In all cases shown in Fig. 4, the SSC is small around slack water, and it reaches its maximum around peak flood and peak ebb, suggesting the resuspension of fine sediment from the bed by tidal currents. The peak SSC during ebb is much larger than that during flood, due to the facts that tidal current at peak ebb is larger than that at peak flood and the strong ebb tidal current lasts longer than flood tidal current. It turns out that the magnitude of local SSC is closely related to that of the tidal current. The sediment at the bed in the North Passage, which mainly consists of silt and clay with a median grain size of 7–16 μm (according to the samples taken during August 2008), with critical depth averaged erosion velocity of roughly 0.4–0.5 m s−1 (Li et al. 1998), can be easily re-entrained. Thus, tidal currents play an important role in entrainment and transport of sediment.

Fig. 4
figure 4

Vertical profiles of current velocity and SSC at station CS3 during a tidal cycle. Plus sign means seaward flow and minus sign means landward flow. Left panels display the condition in wet seasons, while right panels display the condition in dry seasons. Upper two rows display the condition prior to the DWP, while lower two rows display the condition after the DWP. Black dotted lines indicate the time when estuarine turbidity maximum was well developed in the North Passage

Full size image

The vertical distributions of SSC during wet season and dry season differ significantly. The distribution of the SSC during wet seasons is characterized by strong vertical gradients, while SSC is more vertically mixed during dry seasons. The reason is that the water during wet seasons (summer when the temperature is high) contains more organic matter, which triggers the flocculation of fine sediment (Xia and Eisma 1991) and these flocs rapidly settle.

The changes in the characteristics of the SSC cycle prior to and after the DWP involve three aspects. First, the peak bottom SSC doubled during wet seasons, while little change occurred during dry seasons, thus resulting in more significant seasonal cycle of the SSC after the DWP. Second, prior to the DWP, the vertical and time averaged SSC during flood or ebb in the wet season is much smaller than that in the dry season, while after the DWP, the averaged SSC during flood or ebb in the wet season is even larger than that in the dry season. Finally, during dry seasons, peak SSC occurred in the near bottom layer prior to the DWP, while after the DWP, it occurred in the bottom layer.

3.1.2 Longitudinal and vertical distribution of SSC

The ETM was well developed during both flood and ebb. The snapshots of longitudinal–vertical distribution of SSC at the time with maximal SSC during flood and ebb are shown in Fig. 5. The time corresponds to the hours indicated by black dotted lines in the velocity profiles of Fig. 4. The ETM was well developed at peak flood and peak ebb, or 1 h before or after those times. After the DWP, the turbidity maximum is more developed during wet seasons with larger peak SSC at the bottom.

Fig. 5
figure 5

Longitudinal–vertical distribution of SSC (in kilograms per cubic meter) at the time when maxima SSC occurred during flood and ebb, corresponding to the hours with black dotted lines in the velocity profiles of Fig. 4. The triangles denote the location of measurement stations. Left panels display the distributions in wet seasons, while right panels display the distributions in dry seasons. Upper two rows display the distributions prior to the DWP, while lower two rows display the distributions after the DWP

Full size image

In order to compare the location of the ETM prior to and after the DWP, the ETM zone is defined as the region where the near-bed SSC exceeds 2 kg m−3. A 10–15-km upstream shift and extension of the ETM zone occurred after the DWP, and a new ETM core developed at station CS1 in the upper reach. During the wet season, the peak SSC near bed at ETM core increased from 6 to 15 kg m−3 with fluid mud forming around high water and early ebb in the middle reach, while there were minor changes in peak SSC during the dry season.

3.2 Flow components

3.2.1 Residual flow

The spatial distribution of the residual flow in the North Passage is shown in Fig. 6 for the wet and dry seasons prior to and after the DWP. Before the DWP, the residual flow structure in the lower reach was that of a gravitational circulation in both wet and dry seasons, with inflow in the lower layer and outflow in the upper layer. After the DWP, in the wet season, the residual flow structure was significantly modified, characterized by outflow throughout the channel. In contrast, in the dry season, the residual flow structure was still that of a gravitational circulation, with an upstream shift of the zone of landward flow near the bottom. Prior to the DWP, the seaward residual flow was strong in the upper reach and decreased seaward. After the DWP, the seaward residual flow gradually increased from the upper reach to the middle of the lower reach. In Fig. 2, the upper, middle, and lower reaches are defined.

Fig. 6
figure 6

Residual flow (in meters per second) structures in the North Passage. Plus sign means seaward flow and minus sign means landward flow. Left panels display the structures in wet seasons, while right panels display the structures in dry seasons. Top row displays the structures prior to the DWP, while bottom row displays the structures after the DWP

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3.2.2 Tidal current components

Figure 7 shows the spatial distribution of the tidal current components in the North Passage. It reveals that the tidal current was dominated by the M 2 constituent (U M2), followed by the components O 1–K 1 (U O1,K1) and M 4 (U M4), with maximum tidal velocities of 2.3, 0.9, and 0.5 m s−1, respectively. Prior to the DWP, the tidal current amplitudes slightly increased inland in the lower reach and then gradually decreased. After the DWP, they fluctuated considerably along the channel, indicating that the along-channel variation of the tidal dynamics in the North Passage became more complicated due to the engineering works. Overall, the amplitude of the M 2 tidal current considerably increased due to the converging of flow by training walls and groins. There was a slight decrease in the amplitude of the O 1–K 1 tidal current, while there was no significant change in the amplitude of M 4 tidal current.

Fig. 7
figure 7

Spatial distributions of tidal currents (in meters per second) in the North Passage. Here, U O1,K1,U M2,U M4 are the amplitudes of diurnal tidal current, semi-diurnal tidal current, and quarter-diurnal tidal current, respectively. Left panels display the distributions in wet seasons, while right panels display the distributions in dry seasons. Upper three rows display the distributions prior to the DWP, while lower three rows display the distributions after the DWP

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3.3 Suspended sediment concentration components

3.3.1 Mean suspended sediment concentration

The pattern of the mean suspended sediment concentration, denoted by C 0, is shown in the top panels in Fig. 8. During wet seasons, the suspended sediment was trapped in the near bottom layer, and it decreased sharply to the surface. After the DWP, the peak bottom SSC increased from 2.5 to 5 kg m−3 in the wet season, and the vertical mixing was slightly enhanced, leading to an overall increase of the mean SSC in the entire channel. During dry seasons, the suspended sediment was more vertically mixed. The peak bottom SSC was around 2.3 kg m−3 both before and after the DWP during dry seasons, but the vertical gradients of SSC increased, resulting in a decrease in the SSC in the middle and upper layers. The tidal mean SSC distribution during wet seasons after the DWP also shows an upstream extension and shift of the ETM.

Fig. 8
figure 8

Amplitudes of SSC components (in kilograms per cubic meter) in the North Passage. Here, C 0 is the mean concentration, C O1,K1, C M2, C M4 are the amplitudes of SSC components related to diurnal tide, semi-diurnal tide, and quarter-diurnal tide, respectively. Left panels display the distributions in wet seasons, while right panels display the distributions in dry seasons. Upper four rows display the distributions prior to the DWP, while lower four rows display the distributions after the DWP

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3.3.2 Suspended sediment concentration components related to tides

The instantaneous SSC varied significantly during the tidal cycle in the North Passage, as shown by the distribution of amplitudes of SSC components related to tidal constituents O 1–K 1, M 2, M 4 in Fig. 8, denoted by C O1,K1, C M2, C M4. During wet seasons, the peak SSC value of each tidal component reached almost half of the peak value of the mean SSC, except the M 4 component prior to the DWP. During dry seasons, the peak SSC value of each tidal component equaled 15–25 % of the peak value of the mean SSC prior to the DWP and 30 % of the peak value of the mean SSC after the DWP. Amplitudes of tidal SSC components increased significantly after the DWP. During the wet season, the peak values of C M2 and C O1,K1 doubled, and the peak value of C M4 even tripled. During the dry season, the peak value of C O1,K1 doubled, and there was no significant change in C M2 and C M4.

3.4 Net sediment flux and transport

3.4.1 Patterns of net sediment flux

The patterns of net sediment fluxes in the North Passage due to individual mechanisms, involving residual flow and various tidal pumping mechanisms, are presented in Fig. 9. The magnitudes of the net sediment fluxes reveal that residual flow and M 2 tidal pumping were dominant forcing agents in all cases. O 1–K 1 tidal pumping also had a large effect on sediment fluxes during the wet season prior to the DWP.

Fig. 9
figure 9

Spatial structures of residual sediment fluxes (in kilograms per square meter per second) due to individual forcings in the North Passage. Plus sign means seaward flux and minus sign means landward flux. Here, F 0 is the residual sediment flux due to residual flow, and F O1,K , F M2, F M4 are fluxes due to tidal pumping mechanisms related to diurnal tide, semi-diurnal tide, and quarter-diurnal tide, respectively. Left panels display the structures in wet seasons, while right panels display the structures in dry seasons. Upper four rows display the structures prior to the DWP, while lower four rows display the structures after the DWP

Full size image

During the wet season prior to the DWP, the structure of the net sediment flux due to residual flow resembled that of the gravitational circulation, with seaward sediment flux landward of the null point (a place where the tidal and river flows meet and converge) and a two-layer sediment flux seaward of that point, leading to sediment trapping near the null point. The net sediment flux due to O 1–K 1 tidal pumping turned out to be divergent, but the seaward sediment flux in the lower reach was much stronger than landward sediment flux in the upper reach. The net sediment flux due to M 2 tidal pumping was convergent, causing sediment trapping near the point of convergence. The net sediment flux due to M 4 tidal pumping had a similar pattern as that of O 1–K 1 tidal pumping, albeit with a smaller magnitude. Overall, the net sediment flux was dominated by seaward directed components due to residual flow and M 2 tidal pumping in the upper reach and by landward directed components due to residual flow and M 2 tidal pumping in the lower reach. This resulted in sediment trapping in the middle and lower reach.

During the wet season after the DWP, the net sediment flux due to residual flow was directed seaward throughout the channel. The M 2 tidal pumping induced an overall landward net sediment flux, with local exceptions in the lower layer of the upper and lower reach. The other two tidal pumping mechanisms both resulted in divergence of net sediment flux, with local exceptions at the bottom, but their magnitudes were an order smaller than that of previous two fluxes. Thus, the total net sediment flux was dominated by a seaward directed component due to residual flow in the upper reach and a landward directed component due to M 2 tidal pumping in the middle reach, resulting in sediment trapping in the middle reach. Local sediment convergence due to various tidal pumping mechanisms caused weak sediment trapping in the upper reach.

During the dry season prior to the DWP, the net sediment flux due to residual flow displayed the same distribution as that during the wet season. The net sediment flux due to M 2 tidal pumping had a divergent pattern. The net sediment flux due to M 4 tidal pumping was directed landward in the lower layer and seaward in the upper layer with small magnitudes. The divergent net sediment flux due to O 1–K 1 tidal pumping was negligible. Therefore, the total net sediment flux was dominated by components due to residual flow and M 2 tidal pumping, which opposed each other in the upper reach and lower layer of the lower reach, but were both seaward directed in other areas. Trapping of sediment at the bottom resulted from fluxes due to the residual flow and M 4 tidal pumping.

During the dry season after the DWP, the general structures of net sediment flux due to residual flow and M 2 tidal pumping did not change. However, the zone with landward sediment flux induced by residual flow in the lower layer shifted landward and separated into two parts, one in the upper reach and the other in the middle reach. In the upper and middle reach, the seaward sediment flux due to residual flow significantly decreased, while the area with landward sediment flux due to M 2 tidal pumping had a downward extension. Thus, in the upper and middle reach, the total net sediment flux was dominated by landward directed sediment flux due to M 2 tidal pumping, and it was enhanced by the landward directed flux due to residual flow at the lower layer, leading to trapping of sediment in this reach.

3.4.2 Net sediment transport

Net sediment transports induced by individual physical mechanisms and the total net sediment transport in the main channel of the North Passages are shown in Fig. 10. Besides the net transports generated by the residual flow (T 0) and various tidal pumping mechanisms (T O1,K1, T M2, T M4), due to the triple correlations of sea level variation, currents, and SSC, three other transport terms arise, which are the transport \( {T_{{\eta u{C_0}}}} \) as a consequence of the correlation between horizontal and vertical water motion acting with the mean SSC, the transport \( {T_{{\eta c{U_0}}}} \) due to the correlation between tides and tidal components of SSC acting with residual flow, and the transport \( {T_{{\eta cu}}} \) due to the triple correlation of tidal components of sea level variation, velocity, and SSC. These three transport terms measure the contribution of sea level variations to the net sediment transport. The term \( {T_{{\eta u{C_0}}}} \) produced strong landward sediment transport, especially during dry seasons, thereby contributing to sediment trapping. Hereafter, this term is called the Stokes transport. The term \( {T_{{\eta uc}}} \) also induced landward sediment transport but with a much smaller magnitude whose maximum is around 0.3 kg m−1 s−1. The magnitude of \( {T_{{\eta c{U_0}}}} \) is in order of 0.01 kg m−1 s−1, with maximum of around 0.05 kg m−1 s−1 in all cases, which is negligible.

Fig. 10
figure 10

Along-channel distribution of net sediment transport per unit width (in kilograms per meter per second) in the North Passage. Plus sign means seaward transport and minus sign means landward transport. Here, T 0 is the net sediment transport due to residual flow, \( {T_{{\eta u{C_0}}}} \) is the Stokes transport, and \( {T_{{\eta cu}}} \) is the net transport due to the triple correlation of tidal components of sea level variation, velocity, and SSC. Further, T O1,K1, T M2, and T M4 are net transports due to tidal pumping mechanisms related to diurnal tide, semi-diurnal tide, and quarter-diurnal tide, respectively, and T is the total net sediment transport. Left panels display the distributions in wet seasons, while right panels display the distributions in dry seasons. Top row displays the distributions prior to the DWP, while bottom row displays the distributions after the DWP

Full size image

During the wet season prior to the DWP, net sediment transport was dominated by seaward directed components due to residual flow, O 1–K 1 tidal pumping and M 4 tidal pumping, a landward Stokes transport, and a transport due to M 2 tidal pumping that was seaward in the upper reach and landward in the lower reach. The net transport due to residual flow significantly decreased seaward and changed into a weak landward transport at station CS4. Overall, the total net downstream sediment transport decreased seaward, suggesting accumulation of the riverine suspended sediment throughout the channel. During the wet season after the DWP, net sediment transport was mainly composed of a seaward directed component due to residual flow and landward directed components due to M 2 tidal pumping and Stokes transport. The total sediment transport was convergent, indicating sediment accumulation in the middle reach.

During the dry season prior to the DWP, net sediment transport was dominated by a seaward directed component due to residual flow, a landward Stokes transport, and a divergent transport due to M 2 tidal pumping that was directed landward in the upper reach and directed seaward in the lower reach. The total net downstream sediment transport gradually increased seaward in the middle and lower reach, indicating erosion of the river bed in that reach. During the dry season after the DWP, net sediment transport was also dominated by a seaward directed component due to residual flow, a landward Stokes transport, and a divergent transport due to M 2 tidal pumping which was directed landward in the upper reach and directed seaward in the lower reach. The total net sediment transport was divergent, indicating sediment entrainment in the upper and middle reach (CS1–CS7). However, the net landward sediment transport decreased inland at the entrance (CS1–CS0) and the net seaward sediment transport decreased seaward in the lower reach (CS7–CS4); hence, sediment accumulation occurred in these reaches.

Thus, the significant changes occurred in the net sediment transport components due to residual flow and M 2 tidal pumping prior to and after the DWP. The seaward net transport due to residual flow significantly decreased in the upper reach but increased in the lower reach. Consequently, the seaward decreasing net transport changed into seaward increasing transport. During wet seasons, the magnitudes of the main net sediment transport components almost doubled, and net sediment transport due to M 2 tidal pumping changed, from being seaward in the upper reach and landward in the lower reach to being landward almost in the entire domain.

3.5 Main residual components and their sediment transport

Since the residual flow and the net sediment transport it induces have been greatly modified by the DWP, it is important to clarify and identify the main causes for these changes. For this, the changes that occurred in the main residual flow components and their sediment transport is discussed, which are forced by density gradient, river discharge, net tidal mass transport, tidal rectification, and asymmetry in tidal mixing. These residual flow components were derived by the analytical model presented in Section 2.2, and the values of eddy viscosity and slip number used are shown in Table 2. The comparison between the observed and modeled M 2 tidal current is presented in Fig. 11. Besides, the value of absolute error (G in Eq. 24) and relative error (RE in Eq. 25) are presented in Table 2 to show the performance of the model. It turns out that the relative error is about 15–25 %, so the model performance is satisfactory, considering the aims for which it has been designed, i.e., gaining fundamental insight. The structures of residual flow components are presented in Figs. 12 and 13, and net sediment fluxes that they induced are presented in Figs. 14 and 15. The net sediment transports caused by individual agents are shown in Fig. 16. Since the magnitude of residual component due to stress-free surface condition is much smaller than that of other components, it is not discussed here.

Table 2 Vertical eddy viscosity coefficient and slip parameter
Full size table
Fig. 11
figure 11

The comparison between the observed and modeled amplitude of M 2 tidal velocity and phase difference between the semi-diurnal horizontal and vertical tide. The dashed lines represent model predictions; the dots show measured data at various measuring locations. The left panels represent amplitude of M 2 tidal velocity along the estuary, and the red and blue colors represent the predicted and measured velocity at the surface and vertical mean velocity, respectively. The right panels depict relative phase shift between the free surface elevation and vertical mean along-channel velocity component

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Fig 12
figure 12

Residual flow components (in meters per second) due to individual forcings in the North Passage prior to the DWP. Plus sign means seaward flow and minus sign means landward flow. u d, u q, u s, u t, and u a are residual flows due to density gradient, river discharge, Stokes return flow, tidal rectification, and asymmetry in tidal mixing, respectively. Left panels display the structures in wet seasons, while right panels display the structures in dry seasons

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Fig 13
figure 13

Residual flow components (in meters per second) due to individual forcings in the North Passage after the DWP. Plus sign means seaward flow and minus sign means landward flow. u d, u q, u s, u t, and u a are residual flows due to density gradient, river discharge, Stokes return flow, tidal rectification, and asymmetry in tidal mixing, respectively. Left panels display the structures in wet seasons, while right panels display the structures in dry seasons. The salinity data were not obtained in February 2009, so two plots are missing in the right panels

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Fig. 14
figure 14

Structure of residual sediment flux (kilograms per square meter per second) due to individual residual components in the North Passage prior to the DWP. Plus sign means seaward flux and minus sign means landward flux. F d, F q, F s, F t, and F a are residual sediment fluxes due to density gradient, river discharge, Stokes return flow, tidal rectification, and asymmetry in tidal mixing, respectively. Left panels display the structures in wet seasons, while right panels display the structures in dry seasons

Full size image
Fig. 15
figure 15

Structure of residual sediment flux (kilograms per square meter per second) due to individual residual components in the North Passage after the DWP. Plus sign means seaward flux and minus sign means landward flux. F d, F q, F s, F t, and F a are residual sediment fluxes due to density gradient, river discharge, Stokes return flow, tidal rectification, and asymmetry in tidal mixing, respectively. Left panels display the structures in wet seasons, while right panels display the structures in dry seasons

Full size image
Fig. 16
figure 16

Along-channel distribution of net sediment transport per unit width (kilograms per meter per second) in the North Passage due to main residual components. Plus sign means seaward transport and minus sign means landward transport. T d, T q, T s, T t, and T a are sediment transports driven by density gradient, river discharge, Stokes return flow, tidal rectification, and asymmetry in tidal mixing, respectively. Left panels display the distributions in wet seasons, while right panels display the distributions in dry seasons. Top row displays the distributions prior to the DWP, while bottom row displays the distributions after the DWP

Full size image

3.5.1 Density-driven flow

A gravitational circulation results from a balance between pressure gradient (caused by horizontal density gradients and surface slopes) and vertical mixing. Due to the fact that no salinity data were obtained in 2009, the density-driven flow and its sediment transport are missing at the top of the right lower panel of Figs. 12 and 13. The structure of the gravitational circulation did not change of course, with a landward flow at the lower layer and a seaward flow at the upper layer (u d in Figs. 12 and 13). Note that the flow was rather week, consistent with what was found in other studies (cf. Chernetsky et al. 2010; Cheng et al. 2011). Nevertheless, during wet seasons, the location of maximum density gradient after the DWP had a slight upstream shift compared to that prior to the DWP. The landward net sediment flux in the lower layer is much stronger than that of the seaward sediment flux in the upper layer (F d in Figs. 14 and 15). Thus, it caused a landward net sediment transport, but the magnitude of transport was small, smaller than 0.1 kg m−1 s−1 (Fig. 16).

3.5.2 River discharge

The residual flow induced by river discharge depends on the freshwater discharge at the landward side of the North Passage and the variation in the area of the cross section. Due to the frictional effects of the groins and the decrease in the volume of the North Passage, there was a significant decrease in the ebb flow diversion to the North Passage at the bifurcation node of the South Channel (Jiang et al. 2012). Consequently, the freshwater input to the North Passage decreased, although the river discharge at the head of the estuary did not change much. The river discharge at the landward side of the North Passage decreased from 12,670 to 7,950 m3 s−1 in wet seasons (June 1999 to August 2008) and decreased from 3,324 to 2,485 m3 s−1 in dry seasons (February 2000 to February 2009).

Due to decreased river inflow at the entrance, u q (Figs. 12 and 13) in the upper reach significantly decreased. Prior to the DWP, u q gradually decreased seaward because of the discharging of flow into adjacent shoals and channels and expansion into an increased cross-sectional area. After the DWP, u q gradually increased seaward in the middle and lower reach because the flow was concentrated in the main channel by training walls and groins, so u q in the lower reach greatly increased compared to that prior to the DWP. The same change occurred in the net sediment transport due to river discharge (T q in Fig. 16), but the change during dry seasons was not as significant as during wet seasons because the magnitude of the river discharge and its change prior to and after the DWP was much smaller.

3.5.3 Stokes return flow

The variation of the water surface and its correlation with tidal currents induces a net landward water transport. To balance this landward water transport, a seaward mean flow occurs, called Stokes return flow. Thus, Stokes return flow is a seaward residual flow, as is shown in Figs. 12 and 13 (u s), and its strength is governed by the strength of the net water transport. During dry seasons, Stokes return flow dominated over river discharge. Prior to the DWP, the variation of u s along the channel was minor, while after the DWP, it varied considerably along the channel, especially during the wet season, with one maximum in the upper reach and the other maximum in the middle reach. Overall, there was a 35 % increase in the magnitude of u s after the DWP.

During wet seasons, prior to the DWP, the net sediment transport due to Stokes return flow (T s in Fig. 16) increased seaward in the upper and middle reach and then decreased in the lower reach, while after the DWP, T s generally increased seaward. During dry seasons, T s dominated over T q and became the most important transport term. Prior to the DWP, T s generally increased seaward, while after the DWP, its along-channel variation was the same as that of u s, with one maximum in the upper reach and the other maximum in the middle reach.

3.5.4 Tidal rectification

The nonlinear advection of along-channel tidal momentum, by both along-channel tidal flow and vertical tidal flow, results in a residual flow component, and the process is called tidal rectification. Here, due to the fact that only horizontal velocity was measured, only the advection of along-channel tidal momentum by along-channel tidal flow is considered. Prior to the DWP, the residual flow due to tidal rectification was rather week (u t in Fig. 12). During the wet season, the pattern of u t was convergent, contributing to sediment accumulation (F t in Fig. 14). During the dry season, the pattern of u t was opposite to that of the gravitational circulation, with outflow in the lower layer and inflow in the upper layer. However, the net sediment transport caused by tidal rectification is minor prior to the DWP (T t in Fig. 16). After the DWP, the residual flow due to tidal rectification increased, especially during the dry season (u t in Fig. 13). The structure of u t and its sediment flux (F t in Fig. 15) was generally convergent, with local divergence. The magnitude of net sediment transport due to tidal rectification (T t) was still much smaller than that of river discharge and Stokes return flow.

3.5.5 Asymmetry in tidal mixing

As appears from Eq. 13a, the correlation between the time-varying eddy viscosity and the curvature of the M2 tidal flow also results in a net flow. The physical origin of asymmetry in mixing is that straining of density by tidal flow leads to larger mixing during the flood (when salt water is advected over fresher water, thus causing an unstable density stratification) and weaker mixing during ebb (Simpson et al. 1990; Stacey et al. 2010; Burchard and Hetland 2010).

Following Cheng et al. (2010), we have modeled eddy viscosity such that it attains its largest value at the end of the flood tide. As shown in Figs. 12 and 13 (u a), this results in a net flow with a pattern that is identical to that of density-driven flow (velocities are landward near the bottom and seaward near the surface), but with significantly larger magnitudes. These results are consistent with what is found both in data analysis (Stacey et al., 2010) and in numerical experiments (Burchard and Hetland 2010; Cheng et al. 2011). The flow u a thus contributes to net landward transport of sediment, as shown in Fig. 16 (T a).

Prior to the DWP, the residual flow due to asymmetric tidal mixing in the wet and dry seasons (u a in Fig. 12) had a similar magnitude, which is five times larger than the value of the density-driven flow. However, with respect to the location of maximum landward flow in the bottom, there was a landward shift from the wet season to dry season. This is also the case for the location of maximum landward sediment flux in the bottom (F a in Fig. 14).

After the DWP, in the wet season, u a increased by nearly 40 %, with an upstream shift of the maximum landward flow. Thus, the net sediment transport due to asymmetric tidal mixing became a more significant contributor to the landward transport of sediment (see Fig. 16). For the wet season, u a was not computed due to the lack of salinity data, but we would expect it to be important for the landward transport of sediment as well.

4 Discussion

The results presented in Section 3 show that the structure of residual flow in the North Passage, which is an important agent driving net sediment transport, has significantly changed. To identify the main causes leading to the change of the residual flow, main residual flow components were derived from an idealized model. Due to the fact that there were still residual flow mechanisms that might be important but not included in the model, such as net flow driven by lateral advection of along-channel momentum (cf. Lerczak and Geyer 2004, Huijts et al. 2009), there is still some difference between the observed residual flow and the sum of the five computed residual components. However, by comparing the change in the residual flow component due to river discharge and the change in the observed residual flow, it turns out that both of their magnitudes experienced a decrease in the upper reach, but an increase in the lower reach after the DWP. Thus, the changes that occurred in the residual flow due to river discharge are the main causes which led to the change in the structure of residual flow and its net sediment transport. The change in the structure of the residual flow in the flood seasons is mainly due to the increased u q in the lower reach, while the upstream shift of the seaward flow zone at the bottom in the dry seasons is mainly due to the decreased u q in the upper reach.

The net sediment transport due to M 2 tidal pumping has also been greatly changed after the DWP during wet seasons. The main contributors to the M 2 tidal pumping are the tidal asymmetry, entering sediment dynamics through the bed shear stress due to presence of residual flow and M 4 tides, temporal and spatial settling lag, and asymmetry in tidal mixing. Thus, these different sources that contribute to M 2 tidal pumping are interesting to study in the near further to identify the main factors that caused the change in net sediment transport due to M 2 tidal pumping.

For the Yangtze Estuary, there is large amount of sediment input from the Yangtze River. Large part of these sediments was trapped in the bar area, where the North Passage is one of the channels intersecting the bar. Thus, large amounts of sediment were trapped in the North Passage. With respect to the sediment transport in the North Passage, the sediment accumulation occurs when the net seaward sediment transport decreases, so strong landward sediment transport is not necessary for the trapping of sediment.

In this paper, the measured changes in internal sediment transport processes (i.e., internal within the NP) were analyzed as a function of the unknown changes in external conditions, i.e., the changes in freshwater distribution and tidal movement in the estuary, affecting the water movement through the NP. These external changes in conditions led to changes in transport processes within the NP.

Finally, it is to be mentioned that the DWP were not the only modifications in the system. Morphological changes in the other channels of the Yangtze Estuary have affected the flow through the North Passage (Jiang et al. 2012). The construction of the Three Gorge Dam, which began to impound water in June of 2003 (Dai et al. 2011), induced the change in the riverine conditions, especially the decrease in sediment input from the Yangtze River. All these interventions had effects on the observed change in the flow structure and sediment transport in the NP. However, during the execution of the DWP, the significant change in flow, sediment transport, and subsequent morphological changes in the NP were mainly due to the DWP, as demonstrated by Jiang et al. (2012).

5 Conclusions

In this paper, the effects of the large-scale interventions on the flow structure, suspended sediment distribution, and its transport along the main channel of the North Passage of the Yangtze Estuary have been studied, with focus on explaining the changes in net sediment transport in terms of physical mechanisms. For this, field data in wet and dry seasons prior to and at the end phase of DWP were collected and analyzed by combining methods of harmonic analysis and results of an idealized model. From this, harmonic components of velocity and SSC as well as main residual flow components were obtained, and their roles in net sediment transport were assessed.

During the wet season prior to the DWP, the mean SSC distribution shows that sediment was trapped in the near bottom layer of the middle and lower reach. The net sediment transport components due to residual flow, Stokes transport, and M 2 tidal pumping were responsible for sediment trapping. Among the residual flow components, river discharge and Stokes return flow were the largest contributors to the residual flow and its net sediment transport.

During the wet season after the DWP, sediment was trapped in the lower layer of middle and lower reach. Compared to the situation prior to the DWP, the peak value of mean SSC doubled, and the ETM shifted upstream and extended. The increase in the mean SSC value was induced by the increase in the ebb tidal current velocity in the lower reach due to the engineering works and the increase in the fine sediment availability due to maintenance dredging, which caused stronger re-entrainment of sediment from the bed. The ETM shifted because of changes in net sediment transport components. Sediment trapping was mainly due to landward directed transport components due to M 2 tidal pumping and Stokes transport, as well as a seaward transport component due to residual flow. River discharge, Stokes return flow, and asymmetry in tidal mixing were the main contributors to the residual flow and its sediment transport, with the first two terms causing net seaward transport and the latter causing landward transport. The main reason for the upstream shift of the ETM was that the M 2 tidal pumping and residual flow due to asymmetric tidal mixing resulted in stronger landward transport components, while the upstream extension of the ETM was caused by the decrease in the seaward transport component due to residual flow in the upper reach, which is mainly due to the decrease in the river discharge there.

During the dry season prior to the DWP, the mean SSC also showed sediment accumulation in the middle and lower reach. The along-channel variation of the net sediment transport component due to residual flow (especially the flow due to river discharge) and the net sediment transport component due to Stokes transport were responsible for sediment trapping. Besides, residual flow component from asymmetric tidal mixing also contributed to sediment trapping by inducing a landward sediment transport. The sediment was more vertically mixed, and the zone of high SSC was more horizontally expanded compared to that in wet seasons, when sediment dynamics is strongly affected by flocculation processes.

During the dry season after the DWP, there was a slight upstream extension of the ETM, with minor decrease in the values of SSC compared to that prior to the DWP. Sediment trapping was mainly caused by net sediment transport components due to M 2 tidal pumping, Stokes transport, and residual flow. Stokes return flow, river discharge, and tidal rectification were the main contributors to the residual flow and its net sediment transport. The reason for the upstream extension of the ETM was the same as that during wet seasons, but the extension in the dry season is minor compared to that in the wet season because the river discharge is overwhelmed by Stokes return flow among the seaward transport components in the dry season.