Constant vorticity water flows with full Coriolis term

Approximations of steady periodic water waves in flows with constant vorticity

We provide high-order approximations to periodic travelling wave profiles and to the velocity field and the pressure beneath the waves, in flows with constant vorticity over a flat bed.

Dispersion relation for water waves with non-constant vorticity

We derive the dispersion relation for linearized small-amplitude gravity waves for various choices of non-constant vorticity. To the best of our knowledge, this relation is only known explicitly in the case of constant vorticity. We provide a wide range of examples including polynomial, exponential, trigonometric and hyperbolic vorticity functions.

Nearly-hamiltonian Structure for Water Waves with Constant Vorticity

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity

Existence of Wilton Ripples for Water Waves with Constant Vorticity and Capillary Effects

In this paper we study the water wave problem with capillary e ects and constant vorticity when stagnation points are not excluded. When the constant vorticity is close to certain critical values we show that there exist Wilton ripples solutions of the water wave problem with two crests and two troughs per minimal period. They form smooth secondary bifurcation curves which emerge from primary b...