Miquel Caballeria

Self-organization mechanisms for the formation on nearshore crescentic and transverse sand bars

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.

Generation and nonlinear evolution of shore-oblique/transverse sand bars

The coupling between topography, waves and currents in the surf zone may self-organize to produce the formation of shore-transverse or shore-oblique sand bars on an otherwise alongshore uniform beach. In the absence of shore-parallel bars, this has been shown by previous studies of linear stability analysis, but is now extended to the finite-amplitude regime. To this end, a nonlinear model coupling wave transformation and breaking, a shallow-water equations solver, sediment transport and bed updating is developed. The sediment flux consists of a stirring factor multiplied by the depth-averaged current plus a downslope correction. It is found that the cross-shore profile of the ratio of stirring factor to water depth together with the wave incidence angle primarily determine the shape and the type of bars, either transverse or oblique to the shore. In the latter case, they can open an acute angle against the current (up-current oriented) or with the current (down-current oriented). At the initial stages of development, both the intensity of the instability which is responsible for the formation of the bars and the damping due to downslope transport grow at a similar rate with bar amplitude, the former being somewhat stronger. As bars keep on growing, their finite-amplitude shape either enhances downslope transport or weakens the instability mechanism so that an equilibrium between both opposing tendencies occurs, leading to a final saturated amplitude. The overall shape of the saturated bars in plan view is similar to that of the small-amplitude ones. However, the final spacings may be up to a factor of 2 larger and final celerities can also be about a factor of 2 smaller or larger. In the case of alongshore migrating bars, the asymmetry of the longshore sections, the lee being steeper than the stoss, is well reproduced. Complex dynamics with merging and splitting of individual bars sometimes occur. Finally, in the case of shore-normal incidence the rip currents in the troughs between the bars are jet-like while the onshore return flow is wider and weaker as is observed in nature.

On the mechanism of wavelength selection of self-organized shoreline sand waves

Sandy shorelines exposed to very oblique wave incidence can be unstable and develop self-organized shoreline sand waves. Different types of models predict the formation of these sand waves with an initially dominant alongshore wavelength in the range 1–10 km, which is quite common in nature. Here we investigate the physical reasons for such wavelength selection with the use of a linear stability model. The existence of a minimum wavelength for sand wave growth is explained by an interplay of three physical effects: (a) largest relative (to the local shoreline) wave angle at the downdrift flank of the sand wave, (b) wave energy concentration at the updrift flank due to less refractive energy dispersion, and (c) wave energy concentration slightly downdrift of the crest due to refractive focusing. For small wavelengths, effects (a) and (c) dominate and cause decay, while for larger wavelengths, effect (b) becomes dominant and causes growth. However, the alongshore gradients in sediment transport decrease for increasing wavelength, making the growth rate diminish. There is therefore a growth rate maximum giving a dominant wavelength, LM. In contrast with previous studies, we show that LM scales with λ0/β (λ0 is the wavelength of the offshore waves and β is the mean shoreface slope, from shore to the wave base), an estimate of the order of magnitude of the distance waves travel to undergo appreciable transformation. Our model investigations show that the proportionality constant between LM and λ0/β is typically in the range 0.1–0.4, depending mainly on the wave incidence angle.

Modeling shoreline sand waves on the coasts of Namibia and Angola

The southwestern (SW) coast of Africa (Namibia and Angola) features long sandy beaches and a wave climate dominated by energetic swells from the Southsouthwest (SSW), therefore approaching the coast with a very high obliquity. Satellite images reveal that along that coast there are many shoreline sand waves with wavelengths ranging from 2 to 8 km. A more detailed study, including a Fourier analysis of the shoreline position, yields the wavelengths (among this range) with the highest spectral density concentration. Also, it becomes apparent that at least some of the sand waves are dynamically active rather than being controlled by the geological setting. A morphodynamic model is used to test the hypothesis that these sand waves could emerge as free morphodynamic instabilities of the coastline due to the obliquity in wave incidence. It is found that the period of the incident water waves, Tp, is crucial to establish the tendency to stability or instability, instability increasing for decreasing period, whilst there is some discrepancy in the observed periods. Model results for Tp = 7-8 s clearly show the tendency for the coast to develop free sand waves at about 4 km wavelength within a few years, which migrate to the north at rates of 0.2-0.6 km yr-1. For larger Tp or steeper profiles, the coast is stable but sand waves originated by other mechanisms can propagate downdrift with little decay.

Frontshear and backshear instabilities of the mean longshore current

An analytical model based on Bowen and Holman [1989] is used to prove the existence of instabilities due to the presence of a second extremum of the background vorticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current, but the frontshear modes are localized closer to the coast than are the backshear modes. Moreover, under certain conditions both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction. Numerical analysis performed on realistic current profiles confirm the behavior anticipated by the analytical model. The theory has been applied to a current profile fitted to data measured during the 1980 Nearshore Sediment Transport Studies experiment at Leadbetter Beach that has an extremum of background vorticity at the front side of the current. In this case and in agreement with field observations, the model predicts instability, whereas the theory based only on backshear instability failed to do so.

Generation and Nonlinear Evolution of Nearshore Oblique Sand Bars

The morphodynamic instability of a plane sloping beach for oblique wave incidence has been studied by using a nonlinear numerical model based on a wave and depth averaged shallow water equations solver with wave driver, sediment transport and bed updating. The depth integrated sediment flux formulation is defined as a stirring factor times the depth averaged current plus a downslope term. Two formulae for the stirring factor have been selected: a constant and a function based on the Soulsby and Van Rijn formula. In each case, oblique bars appear with a specific orientation (up- current or down-current), with specific shapes and with specific migration velocities. Not only the initial formation is described but also the finite amplitude dynamics and, in particular, the saturation of the growth.

Modulated Shear Flow

An analytical model based on Bowen and Holman is used to investigate the existence of instabilities due to the presence of a second extremum of the background orticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current but the frontshear modes are localized closer to the coast than the backshear modes. Moreover, under certain conditions, both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction.