On the relation between Stokes drift and the Gerstner wave
E.N. Pelinovskyb aNational Research University Higher School of Economics, Nizhny Novgorod Branch, B. Pecherskaya str. 25/12, Nizhny Novgorod, 603155, Russian Federation bFederal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
This paper discusses the properties of two-dimensional, nonlinear, potential and vortex waves on the surface of an ideal liquid of infinite depth. It is shown that to quadratic order in the amplitude, the vorticity of the Gerstner wave is equal in magnitude and different in sign to 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 Shrödinger equation can be physically interpreted as the Doppler frequency shift over the vertically averaged Stokes drift current.
Keywords: waves on the water, vorticity, Stokes drift, Gerstner wave, nonlinear Shrödinger equation PACS:47.35.Bb DOI:10.3367/UFNe.2017.03.038089 URL: https://ufn.ru/en/articles/2018/3/f/ Citation: Abrashkin A A, Pelinovsky E N "On the relation between Stokes drift and the Gerstner wave" Phys. Usp.61 307–312 (2018)