Bars

Sedimentary ridges, both symmetric and asymmetric, and generally larger than bedforms that characterize the upper shoreface of coastal zones dominated by waves are called wave-formed bars. They were recognized as early as 1845 on the marine coasts of Europe (Elie de Beaumont), by 1851 in the Great Lakes of North America (Desor), and subsequently on marine and lacustrine coasts worldwide (see Schwartz, 1982, pp. 135–139). However, confusion still surrounds this term because of its use for ridges with a wide range of size, morphology, location, and orientation relative to the shoreline. Also, the term bar has been used in a variety of environments, from subaerial to those dominated by tidal currents or river currents. Furthermore, the present understanding of the origin(s) and dynamics of wave-formed bars is still incomplete.

Shepard (1950) called shore-parallel ridges and troughs longshore bars and troughs, equating them with the terms ball and low of Evans (1940), and associated them with plunging breakers. He emphasized the seasonality of such bars on the west coast of the United States, and subsequently terms such as winter and summer, storm and normal, and storm and swell have been applied to denote the presence or absence of bars. Although a correlation between profile form and storm waves or season may exist in some localities (e.g., Inman et al., 1993), it is not universal. Both barred and non-barred profiles occur at times in some areas, while in others only one profile type may persist throughout the year. There is usually a distinct relaxation time between the forcing conditions and bar adjustment; thus in the short-term, bars are generally in a transient state. In the longer term (years to decades), wave-formed bars represent the equilibrium morphology for many coastal environments.

Bar morphology

Wave-formed bars are most clearly identified as near-symmetrical or asymmetrical undulations in the upper shoreface profile (Figure B5). They occur intertidally and subtidally, and may range in number from one to more than thirty, this number often varying through time. Short and Aagaard (1993) introduced a bar parameter, B*=x _s /gT² tan β to identify the number of bars on a linear sloping shoreface (tan β) terminating at a constant depth at a distance offshore, x_s. When B* < 20, the profile is non-barred, for B*=20–50, 1 bar occurs; for B*=50–100, 2 bars, for B*=100–400, 3 bars; and for B*>400 there are 4 bars. Crest heights above the adjacent trough can range from less than a decimeter (Carter, 1978) to more than 4.75 m (Greenwood and Mittler, 1979). In plan view, they form continuous or compartmentalized, linear, sinuous, or crescentic patterns, and range from shore-parallel to shore-normal in orientation, often producing periodic or rhythmic topography both alongshore and cross-shore. The morphometry of bars has been studied by Greenwood and Davidson-Arnott (1975), Hands (1976), and Reussink et al. (2000) in order to define the equilibrium form and dynamics induced by a specific set of environmental constraints.

Figure B5

Typical barred profiles from a sandy nearshore environment in the Canadian Great Lakes. The profiles were surveyed in successive years along the same transect. Note the differing number and position of the wave-formed bars at the same location, even though the mean beach slope is the same.

Bar classification

A universal classification of wave-formed bars does not yet exist, and indeed it may never be possible to define perfectly mutually exclusive classes. A simple descriptive classification based on morphology and the associated environmental constraints is illustrated in Table B1 (Greenwood and Davidson-Arnott, 1979). The group names are those in common use, and the definitive paper describing each type is cited. Other classifications are based on the concept that bars are part of a temporal sequence of beach profile evolution and that they are scaled to that of the controlling wave process. The morphological sequence is controlled by incident wave energy (high and low frequency) and was identified either through aerial photographs or more recently through video-imagery (e.g., Short, 1979; Lippmann and Holman, 1990; see Figure B6). Many coastal environments do not experience such sequential behavior.

Figure B6

Classification and scaling of sequential upper shoreface morphologies. The equivalence between the contrasting sequences of Wright and Short and Lippmann and Holman is indicated (modified after Lippmann and Holman, 1990).

Ridge and runnel topography (Type I) is found on low-angle, macroto meso-tidal foreshore slopes dominated by surf action and foreshore drainage during the tidal cycle. Although low in amplitude these bars are usually stable in form and position or migrate only slowly. In contrast, the cusp- or bar-type sand waves (Type II) are extremely dynamic, often destroyed during storms and regenerated as the storm wanes and smaller amplitude, longer period waves propagate shoreward. These bars result from surf bores and swash action near the toe of the swash slope (an alternative name is swash bar). Furthermore, they may develop from Type VI bars as they migrate relatively rapidly both alongshore and onshore, and in the latter case may weld to the foreshore (Davis et al., 1972; Aagaard et al., 1998). Note that there is confusion with respect to the term ridge and runnel as used in northwest Europe and North America (Orford and Wright, 1978; Orme and Orme, 1988). Here, the term ridge and runnel is restricted to its initial definition by King and Williams (1949); the forms described by Hayes and subsequent workers (Hayes and Boothroyd, 1969) are classified here as Type II bars.

Type III multiple parallel bars (e.g., Nilsson, 1973; Exon, 1975) and Type IV transverse bars (e.g., Niedoroda and Tanner, 1970; Carter, 1978; Dolan and Dean, 1985) tend to be limited to low-angle shorefaces and small to moderate wave heights, coupled with limited water level shifts. However, they have been identified on more energetic shorelines (Konicki and Holman, 2000).

The number of bars increases with decreasing beach slope (Davidson-Arnott, 1988). The height and spacing of the multiple bars increases in the offshore direction, and bar form is near symmetrical in contrast to the Type II group. Transverse bars run normal or obliquely to the shoreline and can range in length from 3 m up to 4 km, with heights from less than 0.05 m up to 2 m and alongshore spacing of the

Table B1 Bar morphologies and environmental constraints

order of 10⁰–10² m (Carter, 1978; Gelfenbaum and Brooks, 1997). The larger forms may migrate alongshore at rates up to 8 m a⁻¹. Usually, transverse bars are anchored to the shoreline (indeed they appear as an extension of a shoreline protuberance), but Konicki and Holman (2000) recorded the unusual case of transverse bars running offshore from a Type VI bar.

The division of nearshore bars into two groups is based upon size, stability, and the controlling waveform. Type V bars are associated with large plunging breakers, which produce narrow, low amplitude ridges on relatively steep slopes: they lack a well-defined asymmetry and are essentially unstable modifications of non-barred nearshore profiles. Type VI bars, in contrast, are relatively large configurations formed seaward of the low water level. Where there is more than one bar, the distance offshore, depth-of-water over the crest, and bar height all usually increase offshore in a regular manner, although in some cases the height decreases after some offshore distance (Lippmann et al., 1993; Ruessink and Kroon, 1994). The volume of sediment in each bar form usually increases consistently offshore. Type VI bars may be three-dimensional, sinuous-to-crescentic, and the alongshore length scales may range from 10² to 10³ m (Greenwood and Davidson-Arnott, 1975; Bowman and Goldsmith, 1983). Where more than one bar is rhythmic, the alongshore wavelength decreases shoreward.

Bar genesis

The boundary conditions necessary for bar formation depend upon the longer term evolution of the coast, which dictates the nature of the bed materials (grain mineralogy, size, sorting, etc.), the bathymetric setting (slope, exposure, etc.), and the geographic location (wave climate, tidal regime, etc.). Local forcing conditions for bars have been studied both theoretically and empirically, and by experiments in the laboratory and the field (see van Rijn 1998). In general, barred profiles are associated with large values of both wave steepness and wave height-to-grain size ratios, and are associated with the final stages of shoaling and dissipation of wave energy through breaking, and the complex hydrodynamics, which accompany these processes (Wright et al., 1979). Furthermore, the size of wave-formed bars induces a very strong feedback to the shoaling and breaking process. Although cause and effect are far from clear, it is evident that equilibrium bar profiles can exist only where the time-averaged sediment transport (suspended and bedload) is zero everywhere on that profile.

A large number of specific hypotheses have been proposed for bar formation over the last 50 years and all involve mechanisms for convergence of sediment transport; these hypotheses were primarily related to Type V and VI bars and fall into three major groups:

(1) break point hypotheses relate bars directly to wave breaking and result from: (i) a seaward transport of sediment entrained by roller or helical vortices under plunging or spilling breakers, respectively (Miller, 1976; Zhang, 1994; Figure B7); (ii) convergence of sediment at the breakpoint through onshore transport associated with increasing asymmetry and skewness of the high-frequency incident waves and offshore transport through set up induced undertow (Dally and Dean, 1984; Dally, 1987; Thornton et al., 1996). However, Sallenger and Howd (1989) concluded that bars are not necessarily coupled to the breakpoint, but can grow and migrate, while within the inner surf zone, landward to the point of initial breaking.

Figure B7

Bar formation by breaking waves: (A) trough scouring by a roller vortex under plunging breakers and offshore sediment transport converging with sediment driven onshore by shoaling waves (modified after Miller, 1976); (B) trough scouring by oblique vortices generated under spilling breakers (modified after Zhang, 1994).

(2) infragravity wave hypotheses propose that low frequency waves generated within the surf zone (surf beat) or offshore and reflected produce a convergent pattern of drift velocities, which interact with the large incident short wave oscillatory velocities to induce a range of bar forms from two- to three-dimensional crescentic forms (e.g., Bowen and Inman, 1971; Short 1975; Bowen 1980; Holman and Bowen, 1982; Bowen and Huntley, 1984). These waves can be standing or progressive and can be produced in a number of different ways as a result of energy dissipation during breaking and are frequently related to amplitude modulation of the incident wave field (groupiness; Roelvink and Broker, 1993; Reussink, 1998). Alternating scour and deposition by mass transport velocities in the bottom boundary layer generated by standing waves, resulting from the interaction of reflected and incident waves, was shown to occur in the laboratory by Carter et al. (1973; Figure B8). The boundary layer was actually segregated. At the bed, drift velocities converge at nodes, while at some distance above the drift velocities converge at antinodes. Under large waves when bars are most active, suspension transport is dominant and therefore sediment will converge and bars will form at the antinodal position of standing waves (e.g., Bowen, 1980). Reflection of waves in the infragravity range was clearly demonstrated by Suhayda (1974) and shown to relate to bar forms by Short (1975) and Katoh (1984). Sediment moves to null positions in the drift velocity field of low-frequency standing (Figure B9(A)) or progressive edge waves (Figure B9(B)), which are periodic both alongshore and offshore. Recent field measurements have clearly shown the importance of group-bound long waves to suspended sediment transport in barred surf zones (e.g., Osborne and Greenwood, 1992), but isolating the drift velocities associated with these secondary waves is difficult. This second-order drift velocity hypothesis requires one dominant wave frequency, which is not common (see Bauer and Greenwood, 1990 for an exception). However, there are a number of suggestions to overcome this inadequacy of the edge wave hypothesis. Aagaard (1990) has argued for the excitation of cutoff mode edge waves (limited by the beach slope) and selection of the dominant mode as that mode which is closest to the wave group period. A phase coupling between the primary orbital motion of a partially standing long wave and groupy short waves was also proposed by O’Hare (1994) to avoid this requirement of narrow bandedness in the infragravity spectrum. Other mechanisms producing a limited number of edge wave frequencies and modes are topographic control (Kirby et al., 1981; Bryan and Bowen, 1996) and interaction of edge waves and the longshore current (Howd et al., 1992). O’Hare and Huntley (1994) propose a leaky wave origin for an inner surf zone bar, which is relatively insensitive to the group period, incident wave height, and the width of the infragravity spectrum.

Figure B8

Bar formation as a result of mass transport in the boundary layer of a strongly reflected incident wave. The surface wave envelope is shown as well as the circulation within the bottom boundary layer. Bed load will converge at nodes of the surface elevation and suspended load at antinodes. Note: the boundary layer flow is indicated by single-headed arrows; the mean flow is indicated by double-headed arrows.

Figure B9

Bar formation by infragravity waves: (A) net drift velocities associated with standing edge waves and the creation of crescentic bars (modified after van Beek, 1974). (B) dimensionless drift velocities and equilibrium nearshore bathymetry associated with the propagation of two edge wave modes (1 and 2) of the same frequency in the same direction (modified after Holman and Bowen, 1982). Note: y represents the alongshore direction and x the across-shore direction.

(3) self-organization hypotheses propose that processes associated with the complex, nonlinear feedback between the sand bed and the hydrodynamics give rise to a range of topographic forms. For example, alongshore and offshore sediment movement was proposed under meandering or cellular nearshore circulations produced by (i) instability of longshore flows (Figure B10; Barcilon and Lau, 1973; Hino, 1974; Falques, 1991; Damgaard Christiansen et al., 1994); (ii) coupling between morphodynamic instability and mean flows (Deigaard et al., 1999; Vittorio et al., 1999; Falques et al., 2000); and (iii) Bragg scattering from periodic topography (Heathershaw and Davies, 1985; O’Hare and Davies, 1993; Rey et al., 1995; Yu and Mei, 2000). These mechanisms cannot produce bars directly, but require some initial perturbation of the profile. However, it has been shown that some bar characteristics are not well predicted by these models (e.g., the cross-shore/alongshore spacing—see Konicki and Holman, 2000). The nonlinear action between shoaling waves and the bed (Boczar-Karakiewicz and Davidson-Arnott, 1987) was also proposed as a mechanism for generating periodic patterns of sediment transport which matched the spacing and general shape of multi-barred shorelines.

Figure B10

Bar formation due to hydrodynamic instability between longshore currents and the sand bed (modified after Hino, 1974). Note the meandering nature of the longshore flow and the sinuous bar topography that is produced.

The horizontal roller vortex mechanism is most applicable to single Type V bars of the US west coast, and justifies the early correlation of bar formation with wave steepness. Multibarred profiles reflect either multiple breakpoints (Dally, 1980; Davidson-Arnott, 1981) or bar formation by distinct differences in wave energy; for example, an outer bar may be produced under storm waves and an inner bar by less energetic conditions (King and Williams, 1949). Water level shifts and coincident shifts in breaker location could also produce a multiple barred system. Oblique, helical vortices were produced under spilling rather than plunging breakers in the laboratory and could account for both single and multiple barred profiles (Zhang, 1994). However, the mass transport velocities under reflected standing waves would perhaps best explain the formation of Type III multiple parallel bars; simple reflection of the incident waves could not be the cause, since the length scales of the bars would require much longer periods. The theoretical convergence patterns of drift velocities under standing edge waves provide strong support for their role in forming crescentic Type VI bars. Progressive edge waves may be responsible for linear bars of the same group (Huntley, 1980). Further, the edge wave periods necessary to produce the length scales found in nature is of the same order as the well-known surf beat. However, the generation of these trapped modes of oscillation still remains ill-defined, even though field observations of low-frequency peaks in the nearshore energy spectrum have been made on barred coasts and related to the presence of edge waves (Huntley, 1980; Bauer and Greenwood, 1990).

Barred topography has long been associated with the occurrence of cellular nearshore circulations (Shepard et al., 1941), and Hino (1974) proposed that an instability of the fluid sediment interface would generate variations in sediment transport resulting in sinuous or crescentic undulations of the surf-zone bed (Figure B9). Certainly the role of rip-cell circulation in bar dynamics has been well documented for bar- and cusp-type sand waves (Bowen and Inman, 1969; Davis and Fox, 1972; Sonu, 1973; Greenwood and Davidson-Arnott, 1975; Wright and Short, 1984), for transverse bars (Niedoroda, 1973), and for Type VI bars, both crescentic and straight (Greenwood and Davidson-Arnott, 1979). However, it is also possible that the regularity in nearshore circulations is in fact controlled by the presence of edge waves (Holman and Bowen, 1982). Whichever mechanism initiates bars, there will be feedback between the topography and the hydrodynamics, perhaps giving rise to some “hybrid” model of formation (Holman and Sallenger, 1993).

Bar morphodynamics

In general, the smaller the wave-formed bar the more dynamic it is, as there is less sediment involved in morphological changes (Sunamura and Takeda, 1984). However, there is considerable variability in morphodynamic behavior, depending upon bar type, the general environmental constraints, and indeed the antecedent state of the bar (i.e., whether or not it is close to its equilibrium position). Bars also tend to migrate at lower rates as the tidal range increases, since at some stage the bars are being exposed subaerially and remain static at this time. Bar dynamics have generally been related to behavior under specific storm events. However, the magnitude, frequency, and sequencing (chronology) of such events may be important in the nearshore, which as a nonlinear dynamical system, is extremely sensitive to feedback processes (see Moller and Southgate, 1997; Southgate and Moller, 2000; see Elgar, 2001 for an alternative view). There now exist at least two long time series of morphological change: (1) thirty years of annual profiling along 100 km of the Dutch coast (Ruessink and Kroon, 1994); (2) sixteen years of bathy metry recorded at Duck, NC (Plant et al., 1999). Extensive measurements of the cross-shore location, and alongshore bar shape, are now being made successfully on a near continual basis at a number of locations worldwide using video-imagery (e.g., Lippmann and Holman, 1990; van Enckvort and Ruessink, 2001).

Type I bars are relatively stable in general, although landward migration rates of ∼10 m per month have been recorded. Under low energy conditions the ridges have been observed to be: (1) destroyed by storms and regenerated in the post-storm period (Mulrennan, 1992); and (2) formed by storms (Hale and McCann, 1982). Type II bars have been shown to migrate at relatively rapid rates, both onshore and alongshore, and Type III bars migrate also at a relatively rapid rate. Type II, IV, and V VI bars have been shown to occur as part of a temporal sequence of beach evolution by Wright et al., (1979), Wright and Short (1984), Sunamura (1988), and Lippmann and Holman (1990). This sequence ranges from fully dissipative (barred profile) to fully reflective (non-barred profile) wave conditions, and therefore, is related to the surf similarity parameter (ε=a_bω²/g tan ²β; where a_b=breaker amplitude, ω=incident radian wave frequency, g=the gravitational constant, β=beach slope). In the Australian Model, the two-dimensional shore-parallel longshore bar and trough occurs at the fully dissipative beach stage, the rhythmic bar and beach at an intermediate stage, and the non-barred profile occurs at the fully reflective stage. In regions where a more limited range of waves exist, the beach may simply change between one or two stages, and where the environmental constraints are more restrictive still, then the bars may assume only one characteristic morphology. Further refinement of the stage model used the Dean Parameter (Ω=H_b/ω_sT; where H_b=breaker height in meters; ω_s=sediment fall velocity in meters per second; T=wave period in seconds). Barred profiles occurred when Ω<0.85 and non-barred profiles occurred when Ω<0.85 (Wright et al., 1985). Sunamura (1988) used the dimensionless parameter K*=H ²_b gT₂d, where g is the gravitational constant and d is the grain size, to classify sequences dependent upon erosional or accretional beach stages. Erosion is characterized by K* ≥ 20 and is associated with offshore bar migration, slope decreases, and a dissipative state; while 5 ≤ K* ≤ 20 indicates onshore migration and beach accretion. Yet, a further parameter was introduced by Kraus and Larson (1988) to separate barred and non-barred profiles, P=gH ²_o /ω ³_s T, where H_o=offshore wave height. A value of 9,000 separates barred (greater values) from non-barred profiles (Dalrymple, 1992).

Type VI nearshore bars have been found to migrate onshore, offshore, and alongshore, with offshore rates reaching 2.5 m h⁻¹ during storms and erosion/accretion rates of 0.05 m h⁻¹ (Sallenger et al., 1985; Aagaard and Greenwood, 1995). Onshore migration rates are generally smaller, but may still reach 1 m h⁻¹. When the Type VI bars are three-dimensional, they may migrate alongshore at rates up to 10 m per month (Greenwood and Davidson-Arnott, 1975). Ruessink et al. (2000) examined the relative rates of across-shore and alongshore migration using complex empirical orthogonal functions applied to profile data. The alongshore migration rate ranged up to 150 m per day and was strongly related to the alongshore component of the offshore wave energy flux. Short-term variability in bar crest position was shown to be due to changes in the quasi-regular topography, and not to alongshore uniform on-offshore migration. While offshore migration under storms has been clearly related to hydrodynamic forcing, especially the setup-driven undertow (Gallagher et al., 1998) or mean currents modulated by infragravity waves (Aagaard and Greenwood, 1995), the onshore migration of Type VI bars is poorly known. Generally the motion is attributed to skewed fluid velocities and accelerations (Elgar et al., 2001).

On the Dutch coast a multiple bar Type VI system exhibited characteristics of a feedback-dominated system, producing cyclic changes over either 4 or 15–18 years (Wijnberg and Terwindt, 1995). Plant and Holman (1997) showed that bars on the east coast of the United States exhibited unpredictable behavior in relation to wave height changes and yet still moved through a sequential pattern of form changes. This paradoxical behavior they related to feedback effects. The forcing for these transitions is as controversial as bar genesis, since direct hydrodynamic forcing has been proposed as well as a self-organization mechanism.

Little work has been done specifically upon bar decay, other than the welding process associated with Type II bars (e.g., Davis et al., 1972; Aagaard et al., 1998). However, the one major exception is the study of the multiple bar system along the Dutch coast. Here, the bar system shifts progressively offshore over time and the outermost bar decays. This has been attributed to the action of highly asymmetric, nonbreaking waves (Larson and Kraus, 1992; Reussink and Kroon, 1994; Wijnberg, 1997). Plant et al. (2001) suggest that a morphologic feedback mechanism can lead to bar decay. As bars move onshore under nonbreaking conditions they are also reduced in height; thus they move further away from wave breaking, allowing further bar decay. This has been observed at Duck, NC (Lippmann et al., 1993).

Predictive models of bar genesis and dynamics

Because of the relatively poor knowledge of long-term bar behavior and the inadequacy of local sediment transport models for the complex nearshore environment, predictive models for the genesis and dynamics of wave-formed bars are still far from complete. In general models proposed are either (1) process-based models (e.g., Bowen, 1980), or (2) behavior-based models (de Vriend et al., 1993). The latter range from: (1) highly parameterized models to predict summer-winter (bar-berm) profiles (e.g., Aubrey, 1979) or sequential bar evolution (Wright and Short, 1984; Sunamura, 1988) to (2) statistically based models for predicting bar dynamics (Aubrey et al., 1980) to (3) morphological models to simulate large-scale beach changes (e.g., Cowell et al., 1995).