Three-dimensional oscillatory flow over steep ripples

The process which leads to the appearance of three-dimensional vortex struc tures in the oscillatory flow over two-dimensional ripples is investigated by means of direct numerical simulations of Navier-Stokes and continuity eq uations. The results by Hara & Mei (1990a), who considered ripples of small amplitude or weak fluid oscillations, are extended by considering ripples of larger amplitude and stronger flows respectively. Nonlinear effects, whi ch were ignored in the analysis carried out by Hara & Mei (1990a), are foun d either to have a destabilizing effect or to delay the 'appearance of thre e-dimensional how patterns, depending on the values of the parameters. An a ttempt to simulate the flow over actual ripples is made for moderate Values of the Reynolds number. In this case the instability of the basic two-dime nsional flow with respect to transverse perturbations makes the free shear layer generated by boundary layer separation become wavy as it leaves the r ipple crest. Then the amplitude of the waviness increases and eventually co mplex three-dimensional vortex structures appear which are ejected in the i rrotational region. Sometimes the formation of mushroom vortices is observe d.