A two-dimensional parametrization of a surf zone with a time-dependent breakpoint due to groupiness in the incident wave field is developed. The breakpoint is defined in terms of a mean position X plus a modulation Aa. Free wave solutions are obtained on a plane beach at the group frequency and its harmonics. Shoreward of the breakpoint, standing waves are found, while seaward an outgoing progressive wave exists. The amplitude of the standing wave is relatively insensitive to the incident wave field. The amplitude of the outgoing wave depends on X, the group frequency o, and the beach slope tan •. For certain values of X --(o2X?g tan •) the amplitude of the outgoing wave goes to zero. It appears that any 'resonant' response of the standing wave shoreward of the breakpoint is suppressed by seaward radiation of energy by the outgoing wave.in the onshore-offshore direction.

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Abstract. The coupling between topographic irregularities and wave-driven mean water motion in the surf zone is examined. This coupling occurs because the topographic perturbations produce excess gradients in the wave radiation stress that cause a steady circulation. This circulation, in turn, creates a sediment transport pattern that can reinforce the bottom disturbance and may thereby lead to the growth of large-scale bed forms. To investigate this coupling mechanism, the linearized stability problem with an originally plane sloping beach and normal wave incidence is solved in two different cases. First, the breaking line is considered to be fixed, and second, the perturbations in water depth that produce a displacement of the breaker line are accounted for. The first case shows that the basic topography can be unstable with respect to two different modes: a giant cusp pattern with shore-attached transverse bars that extend across the whole surf zone and a crescentic pattern with alternate shoals and pools at both sides of the breaking line showing a mirroring effect. In the second case, the varying breaker line may have a strong influence on the circulation. This is clear for the giant cusp topography whose growth is totally inhibited. In contrast, the morphology and the growth of the crescentic pattern remains almost unchanged.

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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.