Dispersion relations for gravity water flows with two rotational layers

作者：Martin Calin Iulian^*

来源：European Journal of Mechanics - B: Fluids , 2015, 50: 9-18.

DOI：10.1016/j.euromechflu.2014.10.005

• Dispersion relation
• Discontinuous vorticity
• Stability of the laminar solutions

We derive the dispersion relation for periodic traveling water waves propagating at the surface of water possessing a layer of constant non-zero vorticity gamma(1) adjacent to the free surface above another rotational layer of vorticity gamma(2) which is adjacent to the flat bed. As a by-product we give necessary and sufficient condition for local bifurcation in the frame-work of piecewise constant vorticity. Moreover, we give estimates on the speed at the free surface of the bifurcating laminar flows. These estimates involve only the vorticity gamma(1),the mean depth of water d and the depth at which the jump in vorticity occurs. A stability result for certain laminar flows is also presented.

• 出版日期2015-4