1 Introduction

Buoyancy-driven convection occurs widely in natural phenomena and in many engineering processes. Turbulent Rayleigh–Bénard (RB) convection, is simplified as an idealized paradigm to study convective problems [1,2,3]. In experimental, numerical and theoretical studies, the RB convection is a fluid-filled closed volume, where two parallels generate warm fluid from the bottom-heated layer and cold fluid from the top-cooled layer. In turbulent RB convection, global heat transport and the dynamics of the flow are determined by Rayleigh number (Ra) and Prandtl number (Pr), which are defined as

$$\begin{aligned} Ra={\alpha }{g}\Delta {T}{H}^{3}/({\nu }{\kappa }) \quad and \quad Pr={\nu }/{\kappa }. \end{aligned}$$
(1)

Here, \(\Delta \) T denotes the constant temperature difference across the fluid layer, H the height of the container between plates, g the acceleration due to gravity, and \(\alpha \), \(\kappa \) and \(\nu \) the thermal expansion coefficient, the thermal diffusivity and the kinematic viscosity, respectively. The turbulent heat transport is expressed as Nusselt number (Nu)

$$\begin{aligned} Nu=Q/({\lambda }\Delta {T}/{H}), \end{aligned}$$
(2)

where \(\lambda \) is the thermal conductivity of the convecting fluid and Q is the heat-current density. Many approaches have been achieved to control heat transport, which is of great significance for the technical applications [4,5,6,7,8].

Clustering plumes form self-organized coherence structure, the so-called large-scale circulation (LSC), which spans the convection cell and carries out main transport of heat and mass. Rich fluid-dynamics of the LSC has been seen as a prominent feature of turbulent RB convection and related to natural convection dynamics. Rising and sinking flow structures of the LSC are subjected to the azimuthal motion in the vertical quasi-two-dimensional (2D) plane in cylindrical cells [9,10,11]. In previous experimental studies, low-frequency oscillation is found to associate with the LSC [12,13,14,15]. Mechanisms of azimuthal motion are derived from two ingredients. One is vertically twisting motion of the LSC plane along centreline of the sample [9, 11], and the other is horizontally sloshing motion perpendicular to vertical circulation plane of the LSC [16]. Spontaneous flow reversals lead to irregularly change direction of the LSC, which has access to deeply understand reversal events in geophysical and astrophysical fields [17,18,19,20,21,22,23,24,25].

Convection cells of large aspect ratios \(\varGamma \) facilitate to provide possible flow patterns in experimental and numerical studies. Abundantly coherent structures correspond to various flow topologies and relevant for geophysical flows and industrial applications. Some investigations have been performed in convection cells of aspect ratio \(\varGamma > 1\) and at relatively large Ra. The global velocity field using the particle image velocimetry (PIV) in rectangle cells found that the single-roll structure is broken into the multi-roll structure around \(\varGamma \backsimeq 4\) [26]. Aspect-ratio-4 square cell filled with water is directly measured by the laser doppler velocimetry (LDV) and the PIV, illustrating that two corotating rolls exist and their periodic oscillation is presented [27, 28]. Temperature and horizontal velocity near conducting plate in cylindrical RB convection filled with air indicated that the single-roll mode break down around \(\varGamma = 1.68\) and the double-roll mode switches to the multi-roll mode at about \(\varGamma = 3.66\) [29, 30]. Three-dimensional (3D) numerical simulations in larger aspect ratio cylindrical cells are dominated by the large-scale flow pattern in fully turbulent fields, which is slightly similar to convective circulation cells above the onset of convection [31,32,33]. Massive rolls and cells, known as the superstructure, are identified from removed fluctuations of the temperature and velocity fields, in a wide range of Pr [34]. Furthermore, many features of superstructure are found to be independent of the system geometry in highly turbulent thermal convection [35, 36]. The theory illuminated that the number of the convection rolls and their heat transport depend on Ra and Pr in large-aspect ratio 2D turbulent RB convection [37]. So far, multi-roll pattern and superstructures have not only been reported in turbulent RB convection with large-aspect-ratio cells, but also observed in other turbulent models, such as Taylor-Couette flow, rotating RB convection, pipe flow and channel flow [38,39,40,41,42]. Thus, studies on turbulent RB cells with large aspect ratios are necessary to explore dynamic features of flow structures.

The geometrical shape of the container possesses an important impact on dynamics of flow structure [43,44,45]. Much attention have paid to flow behaviors of the LSC in new-type cells in recent years. The RB experiments with horizontal cylinder cell have been performed [46]. As aspect ratio increases, four flow modes are distinguished from four aspect-ratio regimes [47]. Since there isn’t corners in the vertical cross-section of thin disc cell, corner-vortex effect on the LSC is eliminated. It was revealed that the part of thermal plumes interrupt persistent rotation of the LSC and lead to inverse flow direction[48]. Owing to lack of circular symmetry in a cubic box, orientations of the LSC lock in corner-rotating vortices for long time, and sometimes also switch from one diagonal plane to the other one [49]. For RB annular convection, flow topology, induced by symmetry breaking, occurs spontaneous transition between the quadrupole state and the dipole state [50]. Above of these try to find how large-scale flow structure adopts to sidewall change and uncover underlying flow topology in unconversant shapes. Preliminary study observed that for annular cell of radius ratio \(\eta = 0.5\), but aspect ratio \(\varGamma = 1\), cessations and reversals are absent and orientation of the LSC oscillated in limited coverage, where dynamics of coherent structures were distinguished from known shape of cells [51]. It should be shown clear insight into the dynamics of turbulent RB annular convection with increasing aspect ratios from one. In this paper, we present RB experimental study on flow structures in annular cells with aspect ratios 1, 2 and 4.

The remainder of the paper is organized as follows. Experimental apparatus and methods are described in Sect. 2. Section 3 presents key results of the experimental measurements. We summarize our findings in Sect. 4.

Fig. 1
figure 1

a–c Schematic drawing of annulus convection cell with aspect ratios \(\varGamma =1\), 2 and 4. Dots represent the azimuthal positions of thermistors embedded in the sidewall for a \(\varGamma =1\) (8 thermistors), b \(\varGamma =2\) (16 thermistors) and c \(\varGamma =4\) (16 thermistors). Dotted lines indicate the middle height of cells in experiments. d–f Time-averaged temperature profiles measured by thermistors. The curves are cosinoidal fittings to the data. d \(\varGamma =1\), \(Ra=1.8 \times 10^{10}\). e \(\varGamma =2\), \(Ra=1.6 \times 10^{9}\). f \(\varGamma =4\), \(Ra=2.5 \times 10^{8}\)

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2 Experimental apparatus and methods

Our experiments were carried out in three annular cells of different aspect ratios. The sidewalls consist of two Plexiglas tubes, where the inner cylinder is \(D_{i}=20\) cm diameter and 5 mm thickness, and the outer cylinder is \(D_{o}=40\) cm diameter and 5 mm thickness. Both Plexiglas tubes have an equal height. The heights of three sets of inner and outer cylinders are 40 cm, 20 cm and 10 cm, which correspond to aspect ratios \(\varGamma =\) 1, 2 and 4, respectively. The radius ratio is \(\eta = D_{i}/D_{o}=0.5\), which remain unchanged in three convective cells. The degassed water is adopted as the convecting fluid. The top and bottom plates are made of copper, electroplated with thinner nickel-plated surfaces. A DC power supply (SGI 330X15D) with \(99.99 \%\) long-term stability is used to output heating power. Four Kapton film heaters are sandwiched on bottom conducting plate to support constant and uniform heating. Three layers of Styrofoam are wrapped around the sidewalls. Electrical heating jackets are installed on the outside of Styrofoam to sustain the same temperature of working fluid and possess a temperature stability better than 0.05 \(^{\circ }\)C. Both arrangements safeguard thermal isolation and avoid heat exchange between the convection cell and surrounding environment. A total of 16 thermistors are embedded respectively inside the bottom and top plates to supervise temperature. Those thermistors (Omega, 44032) are connected to acquisition instrument (Keysight, 34972A) at a sampling frequency of 0.33 Hz. The measurement of Ra range is from \(4.2 \times 10^{9}\) to \(4.5 \times 10^{10}\) for \(\varGamma =1\), from \(3.8 \times 10^{8}\) to \(3.2 \times 10^{9}\) for \(\varGamma =2\) and from \(4.8 \times 10^{7}\) to \(4.5 \times 10^{8}\) for \(\varGamma =4\). Experimental measurements are conducted at the Prandtl number \(Pr=4.3\) for \(\varGamma =1\) and \(Pr=5.3\) for \(\varGamma =2\) and \(\varGamma =4\).

The multi-temperature-probe method is used to capture flow structures. Up-flow and down-flow plumes, carrying hot or cold fluid, result in temperature difference in the horizontal plane at mid-height of the cell, which reflects the orientation and strength of flow structures [18, 52]. Blind holes are equally distributed at the mid-height H/2 away from the bottom plate. Thermistors, the same type as those in bottom and top plates, are inserted into the holes. The separation between the fluid-contracted surface and the end of the holes is no more than 1 mm apart. Here, we take into consideration potential multi-roll structure in the condition of increasing aspect ratios from one. More thermistors are employed to accessibly and precisely gain the temperature distribution in these flow states. For \(\varGamma =2\) and 4, 16 thermistors are placed into blend holes from outside the sidewall to measure temperature profile of multi-roll flow. In contrast, instantaneous temperature profile at the height H/2 is monitored by 8 thermistors for \(\varGamma =1\) cell. It is enough to content with the measured demand. Fitting functions are expressed as Eqs. 3 and 4 to fit aziumthal temperature profiles of 8-thermistor in \(\varGamma =1\) and 16-thermistor in \(\varGamma =2\) and 4.

$$\begin{aligned} T_{i}= & {} T_{0}+\delta \text {cos}\left( \frac{{ \pi }}{4} i - \theta \right) \qquad (i=0, 1,...,7), \end{aligned}$$
(3)
$$\begin{aligned} T_{i}= & {} T_{0}+\delta \text {cos}2\left( \frac{{\pi }}{8} i - \theta \right) \qquad (i=0, 1,...,15), \end{aligned}$$
(4)

\(T_{i}\) is the temperature of the ith thermistor. \(T_{0}\) is the mean temperature of all of the thermistors. \(\delta \) is the amplitude of the cosine function, which means the flow strength of the LSC and \(\theta \) is the azimuthal orientation of the LSC defined as the azimutal position of the hot ascending plumes of the LSC. By fitting a cosine function with different periods to mid-height thermistors at each time step, orientations and amplitudes of the flow structure are obtained. In Fig. 1a–c, The shape of annulus convection cells with aspect ratios 1, 2 and 4 are presented. Dotted lines display the mid-height of cells and black dots represent the temperature probes, which are equally distributed azimuthally around the outer cylindrical wall. We plot three typical examples of the time-averaged temperature profiles measured at the mid-height of convection cells, as shown in Fig. 1d–f. The measurement time for the time-averaged temperature profiles varies from 48 to 100 h for each Ra. \(\langle T_{i} \rangle \) is the mean temperature for the ith thermistor and \(T_{c}\) is the average temperature for all the thermistors. Here, \(\langle \cdot \rangle \) stands for a time average. The red curves are the cosinoidal fitting results. The period-one cosine function fits the experiment data for \(\varGamma =1\), \(Ra=1.8 \times 10^{10}\). The period-two cosine function conforms to temperature variations measured by the 16 thermistors for \(\varGamma =2\), \(Ra=1.6 \times 10^{9}\) and for \(\varGamma =4\), \(Ra=2.5 \times 10^{8}\). It is shown that the ejected hot and cold plumes are separated by \(\pi \) in \(\varGamma =1\) cell and similarly, the azimuthal positions of the two ascending hot plumes and two descending cold plumes for \(\varGamma =2\) and \(\varGamma =4\) cells are partitioned by quadrant. For a given aspect ratio of annulus system, the flow structure is statistically long-time stationary turbulent state, which is independent of Ra. It indicates that as \(\varGamma \) is increased from one, the mean flow structures develop from the dipole state to the quadrupole state. Large aspect-ratio annular effects on the dynamics of the two flow structures and their heat-transport properties are need to be further investigated.

3 Results and discussions

We first check how the increasing aspect ratios of annular cells influence the global heat transport. Heat transport of the three cells is conducted systematically by high-precision measurements. Figure 2a shows the results of the measured Nusselt number Nu as a function of Rayleigh numbers Ra for the aspect ratio \(\varGamma =1\) (square), \(\varGamma =2\) (triangle) and \(\varGamma =4\) (circle) in a log-log plot. It is seen that Nu(Ra) of all three data sets can be well described by a power-law scaling \(Nu=0.11Ra^{0.31}\), as the dashed line in this figure. The corresponding compensated \(NuRa^{-0.31}\) is plotted in Fig. 2b in a semilog plot. All three sets of data can be described approximately by a horizontal line in such a range of \(\varGamma \), demonstrating that the global heat transport properties is insensitive to the aspect ratios of the annular cells.

Fig. 2
figure 2

a Measured Nu as a function of Ra for three aspect ratios. The dotted line is the best power law fit \(Nu=0.11Ra^{0.31}\) to all the data. b The corresponding compensated \(NuRa^{-0.31}\) versus Ra in a semilog plot. The squares, triangles and circles represent \(\varGamma =1\), \(\varGamma =2\) and \(\varGamma =4\), respectively

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For comparison, we compare the present results with those obtained previously in cylindrical [53, 54] and rectangular cells [55], as shown in Fig. 3. The annular results descend into the middle of the others. Our data are in excellent agreement with the experimentally measured Nu in different geometries. The slight offsets among the sets of data may result from experimental errors of different systems. For the present parameter ranges, the scaling law between Nu and Ra are still within the so-called classical scaling regime, and thus heat-transport efficiency does not exhibit any significant geometry dependence. This is because the global heat flux is still determined by the dynamics of the thermal boundary layers, which is insensitive to the increasing aspect ratios of the cell’s shape.

Fig. 3
figure 3

Compensated \(NuRa^{-0.31}\) on a linear scale versus Ra on a logarithmic scale. Circles: Present data are the same as Fig. 2. Down triangles: Ref. [53]. Pluses: Ref. [54]. Diamonds: Ref. [55]

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We next discuss whether the aspect ratios of annular geometry affect the global flow strength. As shown in Fig. 1, there are two stable flow states for different values of \(\varGamma \): the dipole state (i.e. the two-roll flow structure) is observed for \(\varGamma =1\), whereas the quadrupole state (i.e. the four-roll flow structure) is detected for \(\varGamma =\) 2 and 4. The convective structures are actuated by thermal plumes organizing from the upper and lower plates. Experimentally, local temperature measurements obtained from conducting plates can detect the impingement of emitting plumes. It is worthy to note that turn-over time \(\psi \) of thermal plumes can be identified directly by the auto-correlation function of the measured plate-temperature time series. The turnover time of autocorrelation function is sensitive to the thermistor position. Only the thermistors embedded in azimuthal positions where cold and hot plumes are emitted from the conducting plates can detect the turnover time. The path length of one single roll of the mean flow is defined as the typical length of the large-scale mean flow. Circulation paths S are \(2H+{\pi } D_{o}\) for the dipole state and \(2H+{\pi } D_{o}/2\) for the quadrupole state. Based on the circulation path and turnover time of the measured temperature, one can calculate the characteristic velocity of the large-scale flow structures. Reynolds number can thus be expressed as \(Re=SH/(\nu \psi )\). In Fig. 4, we plot results of Re as a function of Ra in \(\varGamma =1\), 2 and 4 cells. The the Ra-dependence of the measured Re are fitted as \(Re=0.11Ra^{0.47\pm 0.02}\) (\(\varGamma =1\)), \(Re=0.16Ra^{0.44\pm 0.02}\) (\(\varGamma =2\)) and \(Re=0.06Ra^{0.46\pm 0.01}\) (\(\varGamma =4\)), respectively, as the solid lines shown in the figure. Overall, the fitted scaling exponents are roughly consistent with previous results obtained in cylindrical and rectangular cells [56, 57]. It is remarkable that three scaling laws do not strictly follow a unifying power law in the present parameter ranges. The inset of Fig. 4 plots the corresponding compensated \(ReRa^{-0.46}\) as a function of Ra, the data fall into three different groups, and hence a significant \(\varGamma \)-dependence is evident. These results reveal that the increasing aspect ratios of annular cells have a notable impact on the measured Reynolds number.

Fig. 4
figure 4

Measured Re as a function of Ra for three aspect ratios. Power law fits are \(Re=0.11Ra^{0.47\pm 0.02} (\varGamma =1)\), \(Re=0.16Ra^{0.44\pm 0.02} (\varGamma =2)\) and \(Re=0.06Ra^{0.46\pm 0.01} (\varGamma =4)\). Inset: Compensated \(ReRa^{-0.46}\) for three aspect-ratio sets

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In order to gain a further understanding of how Re varies with the aspect ratio, we analyse the \(\varGamma \)-dependence of Re, reflecting the influence of flow structures on the global flow strength. In the consideration of eliminating the Ra effect, we adopt the scaling Ra with the mean exponent to compensate all the three Re(Ra) data sets. The scaling exponents of Re(Ra) vary between 0.44 and 0.47 with an average value of 0.46. In Fig. 5, \(\overline{ReRa^{-0.46}}\) is plotted as a function of \(\varGamma \), where the overbar denotes the average of \(ReRa^{-0.46}\) for each aspect ratio. The dashed line is the best power-law fit to the data, which shows \(\overline{ReRa^{-0.46}}\sim \varGamma ^{-0.52}\). The inset of Fig. 5 presents the corresponding compensated \(ReRa^{-0.46}\varGamma ^{0.52}\) as a function of Ra for all three \(\varGamma \) data. As one can see, although the measured data is a little bit scatter, different \(\varGamma \) data sets can roughly collapse on a horizontal line within experimental uncertainty. This demonstrates a power-law relation \(Re\sim Ra^{0.46}\varGamma ^{-0.52}\) for the measured Re of the large-scale mean flow.

Fig. 5
figure 5

Average of \(ReRa^{-0.46}\) for each aspect ratio is plotted as \(\overline{ReRa^{-0.46}}\) vs \(\varGamma \). The dotted line is a power law fit to the data yielding \({\overline{ReRa^{-0.46}}}\sim \varGamma ^{-0.52}\). Inset: compensated \(ReRa^{-0.46}\varGamma ^{0.52}\) for all the measured Re data

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To further understand our findings on the large coherent flow structures, we investigate the amplitude \(\delta \) of the two flow structures with varying Ra. The amplitude of the azimuthally aligned rolls is an important step towards understanding properties of the flow states. Based on the analysis of flow states, the amplitude can be conditionally averaged on the two-roll or four-roll structures. Thus, we examine the time-averaged amplitude \(\langle \delta \rangle \) of the dipole and quadrupole states normalized by temperature difference as a function of Ra for three samples, as illustrated in Fig. 6. The two flow states can be described by dissimilarly distinct scaling relations of \(\langle \delta \rangle / \Delta {T} \sim Ra^{-0.40}\) (dipole state) and \(\langle \delta \rangle / \Delta {T} \sim Ra^{-0.82}\) (quadrupole state), respectively. As thermal plumes are the main contribution to the temperature drop detected by the thermistors embedded in the sidewalls at the midplane of the cell, the amplitudes decrease significantly with increasing Ra. Two scaling exponents reflect different properties of flow structures. One sees that the amplitudes of the two-roll flow structure with Ra decrease much faster than those of the four-roll flow structure, which means that the impact dipole state on temperature decline is slightly weaker. For four-roll flow structure, the normalized amplitude with Ra can be described by the same scaling relation for the two cells. Additionally, we note that for both \(\varGamma \) =2 and 4, the two sets agree very well each other in the overlapping range of Ra. The scaling exponent of two-roll flow structure is inconsistent with previous experimental results found by Ref. [58] in a \(\varGamma =1\) cylindrical cell. This implies that although the two-roll flow structure in the annular system corresponds to the single-roll LSC in the cylindrical system, their flow features are different. In addition, in contrast to \(\langle \delta \rangle / \Delta {T}\), the compensated Re in Fig. 5 seems to have a similar tendency for different aspect ratios. This illustrates that although both\(\langle \delta \rangle / \Delta {T}\) and Re can be used to quantify the amplitude of the LSC, they reveal different properties of the LSC, i.e. \(\langle \delta \rangle /\Delta {T}\) is the amplitude of the LSC with respect to temperature drop, while Re reflects the flow strength of the LSC in terms of velocity.

Fig. 6
figure 6

Non-dimensional time-averaged amplitude of flow structures as a function of Ra. Black and red dashed lines represent quadrupole state and dipole state, respectively

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We further examine the energy ratios among different flow modes to reveal the difference between the two flow states. Fourier analysis is applied to the measured azimuthal temperature distribution to obtain high-order modes regarding to high-order flow dynamics [59, 60]. Each Fourier mode corresponds to a special flow state. 8-probe temperature distribution can yield the first four Fourier modes. The first mode is the dipole state, which represents the two-roll flow structure. The second mode is the quadrupole state, showing that the two hot up-flow paths and the two cold down-flow paths organize into the four-roll structure. In analogous cases, the third mode is the sextupole state and the fourth mode is the octupole state. First eight Fourier modes can be identified by 16-probe temperature signatures. As revealed by previous studies, the higher Fourier modes, the lower energy-contained ratios, the first four Fourier modes can fully meet the need of the present analysis. Thus, we only calculate the first four modes for all aspect ratios. Temperature profile T(t) at each time step is adopted by discrete Fourier series. The expression is following as

$$\begin{aligned} T_{k}= & {} T_{0}+\sum _{j=1}^{4} A_{j}\text {cos}\left( \frac{\pi }{4} k - \theta _{j}\right) \qquad (k=0, 1,...,7 \nonumber \\&\quad \text {or} \ 0, 1,...,15), \end{aligned}$$
(5)

\(A_{j}\) and \(\theta _{j}\) represent respectively the amplitude and the phase of the jth Fourier mode, yielding the corresponding amplitudes of the first four modes: \(A_{1}(t)\), \(A_{2}(t)\), \(A_{3}(t)\) and \(A_{4}(t)\). Thus, time-averaged energy of the jth Fourier mode \(\langle E_{j} \rangle \) is determined by \(\langle E_{j} \rangle = \langle A_{j}^{2} \rangle \), according to relation between amplitude Fourier mode and its energy. The sum energy of the flow structure is

$$\begin{aligned} \langle E_{s} \rangle = \langle E_{1} \rangle + \langle E_{2} \rangle + \langle E_{3} \rangle + \langle E_{4} \rangle . \end{aligned}$$
(6)

The energy ratio of each Fourier mode \(\langle E_{ij} \rangle / \langle E_{s} \rangle \) for \(\varGamma \)= 1, 2 and 4 is plotted in Fig. 7. Here, the symbols “i” and “j” represent values of aspect ratios (i=1, 2 and 4) and the jth Fourier mode (\(j=\) 1, 2, 3 and 4), respectively. For \(\varGamma \)= 1, the first mode dominates on the whole, where its mean energy averaged over all Ra is 76.8%, while Ra-averaged energy percentage of the second mode is 18.1%. The third and fourth modes contain much less energy ratio than the first two modes. As Ra increases, energy ratio of the first mode becomes stronger, while energy variation of the second mode trends to the opposite trend. This implies that the first mode extracts the part of energy from the second flow mode with increasing Ra. For comparison, energy-averaged weights of first mode for all the Ra are consistent with the results from previous studies in the cylindrical cell [60]. For \(\varGamma =2\) and 4, the second mode contains the most energy in all modes, whose energy percentage is 84.6% on average. Small fractions contained energy for the first, third and fourth modes are 4.1%, 1.6% and 9.7%, respectively. This illustrates that the four-roll flow structure plays a dominant role and it still persists higher energy weight in \(\varGamma \) =2 and 4 systems. There are obvious difference between the dipole and quadrupole states for energy relative weights of flow modes and these energy variation with Ra. Note that in the cylindrical RB convection, the LSC exhibits twisting motion along the centreline of the cell [61] and horizontally sloshing motion perpendicular to the vertical circulation plane of the LSC [16]. However, due to the different geometrical confinement, we did not observe the twisting or sloshing modes in our annular cells.

Fig. 7
figure 7

Ratio between the time-averaged energy contained in the jth mode \(\langle E_{ij} \rangle \) (\(j=\) 1, 2, 3 and 4) for \(\varGamma =i\) (1, 2 and 4) and the time-averaged sum energy of the flow \(\langle E_{s} \rangle \) as a function of Ra . Red, blue and black are corresponding to \(\varGamma =\) 1, 2 and 4, respectively

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4 Summary

In this paper, we have carried out an experimental investigation of turbulent RB convection filled with water in annular cells with \(\varGamma \)= 1, 2 and 4 over the Rayleigh number range \(4.8 \times 10^{7} \le Ra \le 4.5 \times 10^{10}\). By changing the aspect ratios of annular cells, we observe that the large-scale flow structure exhibits two statistically stable turbulent states, the dipole state (two-roll flow structure) for \(\varGamma =1\) and the quadrupole state (four-roll flow structure) for \(\varGamma =2\) and 4. Measured Nusselt number Nu(Ra), global heat transport, satisfies a power-law scaling \(Nu=0.11Ra^{0.31}\), which is insensitive to the change of annular aspect ratios. However, increasing aspect ratios of annular geometry effects the Reynolds number. The scaling behavior of Re dependence on Ra and \(\varGamma \) is \(Re\sim Ra^{0.46}\varGamma ^{-0.52}\). We explore comparsive studies on the two flow states. By using the multithermal-probe method, we find that the amplitudes of the two flow structures normalized by temperature difference scale \(\langle \delta \rangle / \Delta {T} \sim Ra^{-0.82}\) (dipole state) and \(\langle \delta \rangle / \Delta {T} \sim Ra^{-0.40}\) (quadrupole state). We further investigate energy ratios of Fourier modes for \(\varGamma =1\),2 and 4 systems. For the dipole state, the first mode and the second mode occupies 76.8% and 18.1% of total energy on average, respectively. Additionally, we find that as Ra increases, the first mode becomes stronger, while the second mode comes to weaker in this process, where the first mode obtains the part of energy ratio from the second mode. For the quadrupole state, the second mode dominates account for on average 84.6% in \(\varGamma \)= 2 and 4 cells and other modes are less weight of total flow energy. The findings confirm that two flow structures have distinct difference on turbulent dynamics of annular convection cells. Our investigation provides an example of how increasing aspect ratios of geometry affects the internal flow structures.