The coupling between topography, waves and currents in the surf zone may selforganize 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 depthaveraged 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 (upcurrent 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.

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.

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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, T p , 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 T p = 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 T p or steeper profiles, the coast is stable but sand waves originated by other mechanisms can propagate downdrift with little decay.Key Words: Shoreline evolution, Shoreline sand waves, High angle wave instability, Longshore sediment transport IntroductionShoreline sand waves are undulations of the shoreline that can occur on worldwide coasts, typically showing length and time scales of kilometres and years, i.e., larger than the typical scales of rhythmic surf zone bars , and references therein, for detailed information on surf zone bars). The undulations do not only occur in the shoreline position but the bathymetric contours also undulate with decreasing amplitude up to a certain depth. Shoreline sand waves are episodically or persistently found along various sandy coasts around the world (Bruun, 1954, Verhagen, 1989Inman et al., 1992;Thevenot and Kraus, 1995;Gravens, 1999;Guillén et al., 1999;Stive et al., 2002;Ruessink and Jeuken, 2002;Davidson-Arnott and van Heyningen, 2003; Medellin et al., 2008; Alves, 2009).Shoreline sand waves can be triggered by different physical mechanisms, including forcing by offshore bathymetric anomalies (Gravens, 1999) or periodic input of large quantities of sand due to inlets and rivers (Thevenot and Kraus, 1995). However, sand waves can also emerge from small irregularities of an otherwise rectilinear coast in absence of any forcing at its wavelength. This can occur if the wave climate is dominated by high-angle waves, i.e., waves with a high incidence angle relative to the shore normal, because the rectilinear coast becomes unstable (Ashton et al., 2001, Ashton andMurray 2006a;Falqués et al., 2011). We will hereinafter refer to the mechanism as high angle wave instability and to the resulting shoreline...

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