Dispersion relations for rotational gravity water flows having two jumps in the vorticity distribution

Abstract

We derive the dispersion relation for periodic traveling waves propagating at the surface of water with a layer of constant non-zero vorticity situated between two layers of irrotational flow. Due to the complicated nature of the dispersion relation – a fourth order algebraic equation with intricate coefficients – we also give an estimate of a very simple form involving only the levels at which the vorticity has jumps. Our formula generalizes a corresponding one from [5].