DISPERSION RELATIONS FOR STEADY PERIODIC WATER WAVES OF FIXED MEAN-DEPTH WITH AN ISOLATED BOTTOM VORTICITY LAYER

Abstract

In this paper we obtain the dispersion relations for small-amplitude steady periodic water waves, which propagate over a flat bed with a specified mean depth, and which exhibit discontinuous vorticity. We take as a model an isolated layer of constant nonzero vorticity adjacent to the flat bed, with irrotational flow above the layer.

Keywords:

• Steady water waves
• dispersion relation
• discontinuous vorticity