The existing theory for shore‐transverse rhythmic sand bars relies on morphodynamic instabilities involving the wave‐driven longshore current and rip currents. Intriguingly, transverse finger bars ...are common on coasts with sediment excess, something not related to those currents. Here we show that, if the actual beach profile is above the equilibrium profile, cross‐shore transport can induce an instability triggered by onshore transport together with wave refraction by the emerging bars. We use a numerical model that filters out the dynamics associated to longshore and rip currents but includes a simplified version of cross‐shore transport and is able to reproduce the formation of shore‐transverse bars. The alongshore spacing scales with the wavelength of the incident waves and the cross‐shore extent is approximately equal to the distance from shore to the depth of closure. The modeled bars compare qualitatively well with observations at El Trabucador back‐barrier beach (Ebro delta, Western Mediterranean Sea).
Plain Language Summary
Beaches sometimes exhibit sand ridges (bars) nearly perpendicular to shore that tend to be quite regularly spaced alongshore. Their spacing and cross‐shore extent range from tens to thousands of meters. Intriguingly, these bars develop preferably at beaches with an abundant supply of sand such as delta barrier beaches, barrier islands and estuaries. Here we provide a possible explanation. Due to the sand excess, the bed in these beaches is very flat, the tendency for the sand to move downslope is very weak and the waves push the sand onshore. On the other hand, waves refract, that is, their crest tip on deeper water propagates faster than the tip on shallower water. As a result, they turn toward shallower areas and, thus, the onshore movement of the sand is deflected toward incipient shoals and accumulates there. This causes more intense wave refraction, which in turn brings more sand to the shallows, and so on. In this way, bars can form out of small random irregularities in bed level.
Key Points
Cross‐shore sediment transport in the nearshore can be unstable in the alongshore direction
The morphodynamic instability can develop only for beach profiles above the equilibrium profile
This instability could explain transverse finger bar formation at beaches with sediment excess
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
The dynamics of small‐amplitude perturbations of an otherwise rectilinear coastline due to the wave‐driven alongshore sediment transport is examined at large time and length scales (years and ...kilometers). A linear stability analysis is performed by using an extended one‐line shoreline model with two main improvements: (1) the curvature of the coastline features is accounted for and (2) the coastline features are assumed to extend offshore as a bathymetric perturbation up to a finite distance. For high incidence angles, instability is found in accordance with Ashton et al. (2001). However, it is seen that instability is inhibited by high waves with long periods and gently sloping shorefaces so that in this case the coastline may be stable for any angle. Similarly, there is no instability if the bathymetric perturbation is confined very close to the coast. It is found that the traditional linearized one‐line model (Larson et al., 1987) tends to overpredict the coastline diffusivity. The overprediction is small for the conditions leading to a stable coastline and for moderate incidence angles but can be very dramatic for the conditions favoring instability. An interesting finding is that high‐angle waves instability has a dominant wavelength at the linear regime, which is in the order of 4–15 km, one to two orders of magnitude larger than the length scale of surf zone rhythmic features. Intriguingly, this is roughly the same range of the wavelength of some observed shoreline sand waves and, in particular, those observed along the Dutch coast. A model application to this coast is presented.
The growth of megacusps as shoreline instabilities is investigated by examining the coupling between wave transformation in the shoaling zone, longshore transport in the surf zone, cross‐shore ...transport, and morphological evolution. This coupling is known to drive a potential positive feedback in case of very oblique wave incidence, leading to an unstable shoreline and the consequent formation of shoreline sand waves. Here, using a linear stability model based on the one‐line concept, we demonstrate that such instabilities can also develop in cases of low‐angle or shore normal incidence under certain conditions (small enough wave height and/or large enough beach slope). The wavelength and growth timescales are much smaller than those of high‐angle wave instabilities and are nearly in the range of those of surf zone rhythmic bars, O(102–103 m) and O(1–10 days). The feedback mechanism is based on (1) wave refraction by a shoal (defined as a cross‐shore extension of the shoreline perturbation) leading to wave convergence shoreward of it; (2) longshore sediment flux convergence between the shoal and the shoreline, resulting in megacusp formation; and (3) cross‐shore sediment flux from the surf to the shoaling zone, feeding the shoal. Even though the present model is based on a crude representation of nearshore dynamics, a comparison of model results with existing depth‐averaged two‐dimensional model output and laboratory experiments suggests that the instability mechanism is plausible. Additional work is required to fully assess whether and under which conditions this mechanism exists in nature.
Key Points
Shoreline instabilities can develop in case of low‐angle wave incidence
Morphological coupling between shoaling and surf zones is essential
Space and time scales are comparable to those of rhythmic surf zone features
The 1D diffusion equation for the dynamics of the coastline is revisited. It is found that the classical evaluation of the diffusivity coefficient over‐predicts it by a factor ranging from 1.25 up to ...infinity since the diffusivity may become zero while the classical prediction is always positive. The over‐prediction depends on wave steepness and wave incidence angle. It is larger for swell than for sea waves and it increases with increasing angle. For moderate angles it can easily be about a factor 10. Negative diffusivity occurs in case of large angles, consistent with the large angle morphodynamic instability.
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Sand ridges, with length scales of several km, are prominent features of the seafloor landscape of many sandy continental shelves. Knowledge about the extent to which these ridges influence the ...large‐scale (i.e., decadal and kilometer scales) morphodynamic evolution of the adjacent shoreline and vice versa (shelf‐shoreline morphodynamic coupling) is limited. The present work aims at quantifying this coupling by using a coupled nonlinear shelf‐shoreline model forced by tides and different wave conditions. Model results show that the presence of sand ridges on the shelf creates longshore non‐uniform wave patterns, which act as a forcing template for the morphodynamic development of the shoreline. The shelf‐shoreline coupling primarily works one way, meaning that the morphodynamic evolution of the shelf affects the evolution of the shoreline. When wave propagation is predominantly aligned with the long axis of the shelf ridges, the forced shoreline undulations are so prominent, that they affect the shelf morphology (significant two‐way coupling). Moreover, for those waves, the longshore spacing of the ridges is strongly imprinted on the shoreline morphology. Weaker shoreline undulations develop for waves that propagate more across the ridges and the weakest for time‐varying wave conditions with large variability in their angles of propagation. Model results compare fairly well with observations. Physical mechanisms underlying the different morphodynamic responses of the coupled shelf‐shoreline system to different wave conditions are also given.
Plain Language Summary
Huge sand ridges (scales of 10 kilometers) are observed on the seafloor of many sandy continental shelves. Knowledge about the effects of these ridges on the evolution of the adjacent shoreline is limited. The present study addresses these effects using a coupled shelf‐shoreline model. Model results show that, when waves propagate along the sand ridges, the latter cause the development of large shoreline undulations, which have the same longshore spacing as the ridges. The shoreline undulations are weak for time‐varying wave conditions with large wave directionality (i.e., large variability in their wave angles). Wave climates with a large wave directionality, as is the case of the Belgium coast, are expected to have weak shoreline undulations compared with wave climates with a small wave directionality (e.g., wave climate of Fire Island)
Key Points
Ridges on the shelf provide a forcing template for the large‐scale (decadal and kilometer scales) morphodynamic development of the shoreline
When waves propagate along ridges, strong shoreline undulations develop, which feed back to the shelf morphology (two‐way coupling)
For time‐varying waves with large variability in their angles of propagation, shoreline undulations are small
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
The formation and development of transverse and crescentic sand bars in the coastal
marine environment has been investigated by means of a nonlinear numerical model
based on the shallow-water ...equations and on a simplified sediment transport parameterization. By assuming normally approaching waves and a saturated surf zone,
rhythmic patterns develop from a planar slope where random perturbations of
small amplitude have been superimposed. Two types of bedforms appear: one is a
crescentic bar pattern centred around the breakpoint and the other, herein modelled
for the first time, is a transverse bar pattern. The feedback mechanism related to the
formation and development of the patterns can be explained by coupling the water
and sediment conservation equations. Basically, the waves stir up the sediment and
keep it in suspension with a certain cross-shore distribution of depth-averaged concentration. Then, a current flowing with (against) the gradient of sediment concentration
produces erosion (deposition). It is shown that inside the surf zone, these currents
may occur due to the wave refraction and to the redistribution of wave breaking
produced by the growing bedforms. Numerical simulations have been performed in
order to understand the sensitivity of the pattern formation to the parameterization
and to relate the hydro-morphodynamic input conditions to which of the patterns
develops. It is suggested that crescentic bar growth would be favoured by high-energy
conditions and fine sediment while transverse bars would grow for milder waves and
coarser sediment. In intermediate conditions mixed patterns may occur.
Nearshore oblique sand bars Ribas, F.; Falqués, A.; Montoto, A.
Journal of Geophysical Research - Oceans,
April 2003, Volume:
108, Issue:
C4
Journal Article
Peer reviewed
Open access
The coupling between hydrodynamics and the evolving topography in the surf zone has been theoretically examined for oblique wave incidence. It is shown that positive feedback can lead to the initial ...growth of several types of rhythmic systems of sand bars. The bars can be down‐current oriented or up‐current oriented, which means that the offshore end of the bar is shifted down‐current or up‐current with respect to the shore attachment. In the limit of strong current compared to wave orbital motion, very oblique down‐current oriented b ars are obtained with a spacing of several times the surf zone width. When wave orbital motions are dominant, systems of up‐current oriented bars and crescentic/down‐current oriented bars appear with spacings of the order of the surf zone width. The latter feature consists of alternating shoals and troughs at both sides of the break line with the inner shoals being bar‐shaped and oblique to the coast. The growth (e‐folding) time of the bars ranges from a few hours to a few days and it is favored by constant wave conditions. The range of model parameters leading to growth corresponds to intermediate beach states in between the fully dissipative and the fully reflective situations. Preliminary comparison with field observations shows qualitative agreement.
We present a novel process‐based morphodynamic model, which includes transport processes due to both velocity and acceleration skewness and a new formulation for intrawave motions, that successfully ...simulates observations of onshore sandbar migration. Results confirm findings of previous studies, in which each process was considered separately and in which sediment transport was computed from the observed water motion. However, our results indicate that accounting for the joint action of both velocity and acceleration skewnesses causes major improvement of the modeled onshore bar migration and is essential to accurately model the evolution of the entire cross‐shore bottom profile, when compared with observations. We also demonstrate that the morphodynamics in the shoaling zone are dominated by velocity skewness (bed shear stresses), while sediment transport induced by acceleration skewness (pressure gradients) controls the morphodynamics in the inner surf zone.
Key Points
A novel morphodynamic model describes field‐observed onshore sandbar migration
Both wave velocity and acceleration skewness are equally important
Accelerations control the inner surf zone; velocities dominate the shoaling zone
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
The hypothesis that the formation and dynamics of large scale shoreline sand waves can be explained by a feedback mechanism between waves and nearshore morphology under very oblique wave incidence is ...explored with a quasi 2D nonlinear morphodynamic model. Using constant wave conditions it is found that if the wave incidence angle at the depth of closure is larger than about 45° the rectilinear coastline becomes unstable and a shoreline sand wavefield develops from small random perturbations. Shoreline sand waves develop with wavelengths between 2 and 5 km, they migrate downdrift at about 0.5 km/yr and they reach amplitudes up to 120 m within 13 years. Larger wave obliquity, higher waves and shorter wave periods strengthen the shoreline instability. Cross‐shore transport is essential for the instability and faster cross‐shore dynamics leads to a faster growth of the sand waves. Simulations with variable wave incidence angles (alternating between 60° and 30°) show that a large proportion of high angle waves is required for spontaneous sand wave formation (at least 80%). Insight is provided into the physical mechanism behind high angle wave instability and the occurrence of a optimal length scale for sand wave growth. The generic model results are consistent with existing observations of shoreline sand waves, in particular with those along the southwest coast of Africa.
Key Points
Shoreline sand waves emerge from the feedback between morphology and wave field
Wave angles persistently larger than 45 deg are required at the depth of closure
Sand waves with a length of 2‐5 km and amplitudes up to 120 m develop in 13 yr
Work undertaken in the EU HUMOR project on morphodynamical modelling, particularly with regard to simulating and understanding rhythmic surf zone bars and related morphodynamic self-organization, is ...presented. These features are reviewed and their engineering context stated. Hydrodynamical and morphodynamical models developed and/or applied within the HUMOR project in order to address these issues are briefly presented. The linear stability modelling concept and stability studies using fully nonlinear models are contrasted. The stability of a shore-parallel bar under normal or oblique wave incidence is chosen as a test case for the different models. The results are compared and discussed. Lastly, modelling efforts and main results from the project are summarized. Recommendations for further work are made.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPUK
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