Oscillating flows over periodic ripples of finite slope

Abstract

The analysis of a laminar oscillating flow over a wavy surface is an important first step toward understanding the complicated dynamics over sand ripples along sea coasts. In a previous paper, two separate asymptotic theories for modestly large Reynolds numbers were presented, one for finite ripple slope but small Keulegan-Carpenter number, the other for finite Keulegan-Carpenter number but small ripple slope, where the Reynolds number is defined with the ambient oscillation velocity and the ripple amplitude, and the Keulegan-Carpenter number is the ratio of the oscillation amplitude to the ripple wavelength. Different types of vortex motion were found above the ripples. Here, a seminumerical solution of the Navier-Stokes equations in power series of the ripple slope, with emphasis on the intermediate regime where both parameters are finite and the Reynolds number is from order unity to moderately large is presented. For moderately large Reynolds number, the present results are similar to the second asymptotic theory in which there are two boudary layers with an oscillating vortex high above the rippled bed. For relatively small Reynolds numbers of order unity, the Stokes and the outer layers merge. In addition, the presence of bed ripples is found to increase the rate of energy dissipation by as much as 40%. © 1992 American Institute of Physics.