Generation of sand ripples and sand bars by surface waves

Abstract

Part I Generation of Sand Ripples by Surface Waves In Chapter 1, we study the sand ripple instability under partially standing surface waves in constant water depth. For gently sloped ripples, the approximate flow field is· worked out. By invoking an empirical formula of sediment transport rate, an eigenvalue problem is obtained, which gives rise to the equation for initial ripple growth with coefficients depending on local wave conditions. It is found that the wave-induced steady streaming has no effect on ripple growth. Thus, ripple instability is locally similar to the cases for oscillatory flows and for purely progressive waves, and is driven by ripple-induced flow. But the intensity of this process varies spatially with the period of half the surface wavelength due to the reflection. The results show that beneath the envelope minima (nodes) ripples grow the fastest and are the longest; under the envelope maxima (antinodes) ripples are unlikely. Part II Generation of Sand Bars and Sediment/Wave Interaction In this part we study the formation mechanism of sand bars under reflected surface waves and the mutual influence of the waves and bars through Bragg resonance. In Chapter 2, we first give an analysis of the effects of shoreline reflection on Bragg resonance by considering rigid bars, aiming at acquiring a deeper understanding of the physical processes of the Bragg resonance mechanism. We show that finite reflection by the shoreline can increase the wave energy arriving at the shore, in contrast to the result from most previous studies, suggesting that the mechanism can enhance the attack of the incident sea on the beach. The phase relation of the rigid bars and the shoreline reflection is found to be a key to the qualitative change of wave response. In Chapter 3, we develop a quantitative theory to describe the formation mechanism of sand bars by coupling sediment dynamics and wave hydrodynamics. Assuming that the slopes of waves and bars are comparably gentle and sediment motion is dominated by the bedload, an approximate evolution equation of bar height is derived. This equation shows that sand bars grow and evolve via a forced diffusion process rather than instability. Both the forcing and diffusivity depend on the flow field above the current bed. In Chapter 4, the coupled evolution of sand bars and waves is investigated, in which the Bragg scattering mechanism has been understood as two concurrent physical processes: energy transfer between two wave-trains propagating in opposite directions and change of their wavelength. Both effects are found to be controlled locally by the position of bar crests relative to wave nodes. In the absence of shoreline reflection, it is found that pre-existing sand bars cannot be maintained by their own Bragg scattered waves and the formation of sand bars offshore by Bragg scattering is at best a transient phenomenon. Comparison with experimental data supports the description of bar formation as a forced diffusion process. In Chapter 5, we examine the effects of horizontal variation of eddy viscosity on the evolution of bars. This variability arises because (1) the intensity of wave oscillation at the bottom changes in space due to the reflection; (2) the bottom roughness is not uniform due to the formation of ripples. While the forced diffusion mechanism is not changed qualitatively, it is found that the variable turbulent intensity inside the wave boundary layer strongly enhances the spatial fluctuation of the sand flux induced by wave stresses, thus causes stronger forcing to the bar growth.