## Vertical Fluxes Induced by Weak-Nonlinear Internal Waves in a Baroclinic Flow

*A.A. Slepyshev*

Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation

### Abstract

In a Bussinesq approximation free internal waves are considered at the account of turbulent viscosity and diffusion in a vertically-non-uniform flow. In linear approximation the dispersive relation and decrement of wave attenuation are found. The equation for amplitude of the vertical velocity, containing small parameter at the higher derivative, proportional to turbulent viscosity, solved by Ljusternik-Vishik asymptotic method. Boundary-layer solution on a vicinity of a bottom and a free surface are found. The non-viscous boundary value problem of the second order is solved numerically according to an Adams's implicit scheme of the third order accuracy. The wave number at the fixed frequency of a wave is found by a shooting method. Stokes drift velocity and vertical wave flux of salt are determined in the second order on wave amplitude. Shift of phases between fluctuations of salinity and vertical velocity with regard to turbulent viscosity and diffusion differs from *π*/2, therefore the vertical wave flux of salt differs from zero. The dispersive parity, decrement of wave attenuation and wave fluxes are calculated for internal waves observed during the 3rd stage of the 44 cruise of R/V "Mikhail Lomonosov" to the northwest shelf of the Black sea. Critical layers for a current profile were absent at the test site (where the measurements were carried out), i.e. phase rate of internal waves exceeded the current velocity. It is shown that out of a layer with the maximum gradient of salinity, i.e. out of surface layer, the wave flux of salt is comparable in absolute value with the turbulent one. In a surface layer turbulent flux of salt exceeds the wave one. The consideration of current results in slight decrease of the wave flux. Horizontal component of Stokes drift velocity, which is transversal to the wave propagation direction, differs from zero and is one order less than longitudinal one when taking into account the current.

### Keywords

internal waves, turbulence, Stokes drift

### For citation

Slepyshev, A.A., 2015. Vertical Fluxes Induced by Weak-Nonlinear Internal Waves in a Baroclinic Flow. *Physical Oceanography*, (1), pp. 59-72. doi:10.22449/1573-160X-2015-1-59-72

### DOI

10.22449/1573-160X-2015-1-59-72

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