The effect of randomness on the stability of capillary gravity waves in the presence of air flowing over water - Majumder, D.P.; Dhar, Asoke Kumar (Zielona Góra: Uniwersytet Zielonogórski)
A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths.
Keywords: capillary gravity waves; randomness; evolution equation; instability