Stability of waves on fluid of infinite depth with constant vorticity

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

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.

Nonlinear Hamiltonian Waves with Constant Frequency and Surface Waves on Vorticity Discontinuities

Waves with constant, nonzero linearized frequency form an interesting class of nondispersive waves whose properties differ from those of nondispersive hyperbolic waves. We propose an inviscid Burgers-Hilbert equation as a model equation for such waves, and give a dimensional argument to show that it models Hamiltonian surface waves with constant frequency. Using the method of multiple scales, w...

Capillary Gravity Waves on the Free Surface of an Inviscid Fluid of Infinite Depth - Existence of Solitary Waves

Existence of solitary internal waves in a two layer uid of innnite depth. Preprint 1995. 17] J.M. Vanden{Broeck & F. Dias. Gravity{capillary solitary waves in water of innnite depth and related free surface ows. 17 The linear operator L im associated with the second equation has also a simple zero eigen-value with eigenfunction A which is even. Therefore, L im is also invertible on odd function...