MODULATION OF GRAVITY-WAVES WITH SHEAR IN WATER

The effect of water shear on the stability of infinitesimal perturbati ons (in the form of side bands) to a finite-amplitude gravity wave is investigated both numerically and analytically. The shear is modeled b y a piecewise-linear velocity profile, Nonlinear cubic Schrodinger equ ation for the wave envelope of a slowly varying wave train is derived. It is shown that depending on the direction of propagation (along or against the shear) of the finite-amplitude waves, the effect of shear on the stability is substantially different. In most cases, however, t he shear strength increase first enhances, but later suppresses, the i nstability.