Unsteady ripple generation on steep gravity-capillary waves

Parasitic ripple generation on short gravity waves (4 cm to 10 cm wavelengt hs) is examined using fully nonlinear computations and laboratory experimen ts. Time-marching simulations show sensitivity of the ripple steepness to i nitial conditions, in particular to the crest asymmetry. Significant crest fore-aft asymmetry and its unsteadiness enhance ripple generation at modera te wave steepness, e.g. ka between 0.15 and 0.20, a mechanism not discussed in previous studies. The maximum ripple steepness (in timew) is found to i ncrease monotonically with the underlying (low-frequency bandpass) wave ste epness in our simulations. This is different from the sub- or super-critica l ripple generation predicted by Longuet-Higgins (1995). Unsteadiness in th e underlying gravity-capillary waves is shown to cause ripple modulation an d an interesting 'crest-shifting' phenomenon - the gravity-capillary wave c rest and the first ripple on the forward slope merge to form a new crest. I ncluding boundary layer effects in the free-surface conditions extends some of the simulations at large wave amplitudes. However, the essential proces s of parasitic ripple generation is nonlinear interaction in an inviscid fl ow. Mechanically generated gravity-capillary waves demonstrate similar char acteristic features of ripple generation and a strong correlation between r ipple steepness and crest asymmetry.