Why are gravity-capillary waves skewed in the way they are?

Presented by Victor Shrira - School of Computing and Mathematics, Keele University, UK

Abstract: In nature the wind waves of gravity-capillary range are noticeably skewed forward. The salient feature of such waves is a   characteristic pattern of capillary ripples on their crests. The   train of these 'parasitic capillaries' is not symmetric with respect   to the crest, it is localised on the front slope and decays towards   the trough. Although understanding the gravity-capillary waves   front-back asymmetry is important for remote sensing and,   potentially, for wave-wind interaction, the physical mechanisms   causing this asymmetry have not been identified. Here we address this gap by extensive numerical simulations of the Euler equations   employing the method of conformal mapping for two-dimensional potential flow and taking into account wave generation by wind and dissipation due to molecular viscosity. On examining the role of   various factors contributing to the wave profile front-back   asymmetry: wind forcing, viscous stresses, the Reynolds stresses   caused by ripples, we found in the absence of wave breaking the   latter to be by far the most important. It is the lop-sided ripple   distribution which leads to the noticeable fore-aft asymmetry of the   mean wave profile. We also found how the asymmetry depends on wavelength, steepness, wind, viscosity and surface tension. The results of the model are discussed in the context of the available   experimental data on asymmetry of gravity-capillary waves in both   breaking and non-breaking regimes. A reasonable agreement of the model with the data has been found for the regime without breaking or microbreaking.

The work was done jointly with A.Dosaev and Yu.Troitskaya.