Unsteady ripple generation on steep gravity–capillary waves

Abstract

Parasitic ripple generation on short gravity waves (4 cm to 10 cm wavelengths) is examined using fully nonlinear computations and laboratory experiments. Time-marching simulations show sensitivity of the ripple steepness to initial conditions, in particular to the crest asymmetry. Significant crest fore–aft asymmetry and its unsteadiness enhance ripple generation at moderate wave steepness, e.g. ka between 0.15 and 0.20, a mechanism not discussed in previous studies. The maximum ripple steepness (in time) is found to increase monotonically with the underlying (low-frequency bandpass) wave steepness in our simulations. This is different from the sub- or super-critical ripple generation predicted by Longuet-Higgins (1995). Unsteadiness in the underlying gravity–capillary waves is shown to cause ripple modulation and an interesting ‘crest-shifting’ phenomenon – the gravity–capillary wave crest and the first ripple on the forward slope merge to form a new crest. Including boundary layer efects in the free-surface conditions extends some of the simulations at large wave amplitudes. However, the essential process of parasitic ripple generation is nonlinear interaction in an inviscid flow. Mechanically generated gravity–capillary waves demonstrate similar characteristic features of ripple generation and a strong correlation between ripple steepness and crest asymmetry.