Numerical simulation of solitary gravity waves on deep water with constant vorticity

We present a numerical study of essentially nonlinear dynamics surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation shear flow is known to have two branches; one which weakly dispersive for long waves. Weakly evolution the this branch can be described by Benjamin–Ono equation, integrable and has soliton multi-soliton solutions. Currently, extent properties such solitary obtained within model are preserved exact Euler unknown. investigate behavior class without restrictive assumption weak nonlinearity equations. localized initial perturbations leading formation single or multiple modeled, finite-amplitude discussed. show that framework equations, two-soliton collisions almost elastic, but contrast solutions receive phase shift as result interaction.