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Regular version of the site

Article

On the relation between Stokes drift and the Gerstner wave

Physics-Uspekhi. 2018. Vol. 61. P. 307-312.
Abrashkin A. A., Pelinovsky E.

We discuss the properties of two-dimensional, non-

linear, potential, and vortex waves on the surface of an ideal

liquid of infinite depth. It is shown that in the quadratic order in

the amplitude, the vorticity of the Gerstner wave is equal in

magnitude to and different in sign from that of the Stokes drift

current in a surface layer. This allows a classic Stokes wave

obtained in the framework of potential theory to be interpreted

as a superposition of the Gerstner wave and Stokes drift. It is

proposed that the nonlinearity coefficient in the nonlinear

SchroÈ dinger equation can be physically interpreted as the Dop-

pler frequency shift along the vertically averaged Stokes drift

current.