Unsteady ripple generation on steep gravity–capillary waves

Parasitic ripple generation on short gravity waves (5 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. This unique unsteady e ect enhances 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 wave steepness in our simulations. This is di erent from the subor super-critical ripple generation predicted by Longuet-Higgins (1995). Modulation in the underlying gravity waves is shown to cause ripple modulation and an interesting \crestshifting" phenomenon | the gravity-wave crest and the rst ripple on the forward slope merge to form a new crest. Mechanically generated gravity-capillary waves demonstrate similar characteristic features of ripple generation and a strong correlation between ripple steepness and crest asymmetry.