Formation of sand bars under surface waves

Abstract

A quantitative theory is described for the formation mechanism of sand bars under surface water waves. By assuming that the slopes of waves and bars are comparably gentle and sediment motion is dominated by the bedload, an approximate evolution equation for bar height is derived. The wave field and the boundary layer structure above the wavy bed are worked out to the accuracy needed for solving this evolution equation. It is shown that the evolution of sand bars is a process of forced diffusion. This is unlike that for sand ripples which is governed by an instability. The forcing is directly caused by the non-uniformity of the wave envelope, hence of the wave-induced bottom shear stress associated with wave reflection, while the effective diffusivity is the consequence of gravity and modified by the local bed stress. During the slow formation, bars and waves affect each other through the Bragg scattering mechanism, which consists of two concurrent processes: energy transfer between waves propagating in opposite directions and change of their wavelengths. Both effects are found to be controlled locally by the position of bar crests relative to wave nodes. Comparison with available laboratory experiments is discussed and theoretical examples are studied to help understand the coupled evolution of bars and waves in the field.

Sandbar formation under surface waves: Theory and experiments

“…The forcing term À@q t 0 /@x 0 , where q t 0 is given in equation (16), is due to the spatial variation of bed shear stresses. A similar equation was derived earlier by Yu and Mei [2000a].…”

“…[15] By reasoning that gravity reduces (increases) the threshold stress if the fluid moves upward (downward) along a slope, Fredsøe [1974] proposed a relation which can be reduced to the form of (6), with an extra factor of Q C % 0.05 in the second term, and has been used by Yu and Mei [2000a] and by Komarova and Newell [2000] in a theoretical model of tidal bars.…”

“…This suggests that sandbars can be generated for any finite seaward reflection, as O'Hare and Davies [1993] found numerically and experimentally. Yu and Mei [2000a] have also shown that if shoreline reflection is not present, sandbars (on the scale of the wavelength) cannot be generated and any residual sandbars present initially are eventually washed out. Therefore, under the conditions of the study, finite reflection from the shore is both necessary and sufficient to generate and maintain sandbars.…”

“…Dulou et al [2000] studied sandbar formation under partially standing waves on a gently sloping bed in a small wave tank. Scaling effects limit the similarity of these small scale sandbars to those observed in the field [Yu and Mei, 2000a]. Also, fine grains were used so that sediment was transported largely in suspension.…”

Laboratory study of wave bottom interaction in the bar formation on an erodible sloping bed

“…The case of a bed load dominated sediment transport has been also studied theoretically [Yu and Mei, 2000a].…”