Nonlinear effects in the process of propagation of internal waves in the presence of turbulence

In the Boussinesq approximation, we study the nonlinear effects observed in the process of propagation of internal waves in the presence of turbulence. The space damping factor of the waves is evaluated. The Stokes drift velocity and the Euler velocity of the mean current induced by waves due to the presence of nonlinearity are determined. It is shown that the principal contribution to the wave transfer is made by the horizontal velocity of the induced current. The Stokes drift is significant only near the bottom. The vertical component of the Stokes drift velocity obtained with regard for the turbulent viscosity is nonzero.     

On some peculiarities of the dispersion properties of internal waves in the ocean

The effect of mean flows on the dependence of the internal waves' group velocity on the wavenumber is considered. Experimental data on the behaviour of internal wave packets propagating in the ocean at an extreme group velocity are reported.Translated by Vladimir A. Puchkin.     

Transport of Sediments Entrapped by Topographic Waves

In the Boussinesq approximation, for topographic waves entrapped by a sloping bottom, we determine mean currents induced by a wave due to nonlinearity with regard for turbulent viscosity and diffusion. We determine the thickness of the bottom boundary layer, the vertical turbulent exchange coefficients, and turbulent stresses on the upper boundary of the boundary layer depending on the parameters of the wave. In the diffusion approximation, we find the vertical distribution of the concentration of sediments suspended by the wave and the flow rates of sediments along and perpendicular to the isobaths. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 13–24, September–October, 2005.     

Characteristics of trapped topographic waves in the northwest part of the Black Sea

We study trapped baroclinic topographic waves in the northwest shelf of the Black Sea for the actual slopes of the bottom and stratification. The time scales of trapped waves are determined. The space scales of the amplitude of oscillations are computed. It is shown that the vertical distribution of the amplitude of oscillations is in qualitative agreement with the experimentally observed distribution. The energy of topographic waves trapped by the sloping bottom is concentrated in the bottom layer, which agrees with the data of measurements. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 44–52, September–October, 2006.     

Heat and mass transport by weakly non-linear internal waves in the presence of turbulence

The method of asymptotic multiscale expansion is applied to determine the mean current velocity and density fields induced by a packet of internal waves. In the limiting case of a weakly non-linear plane wave, heat, salt, and impulse vertical transport is conditioned by the vertical component of the Stokes drift velocity, which is non-zero, when turbulent viscosity and diffusion are considered. As the wave period decreases, the wave fluxes of heat, salt, and impulse increase. In shallow waters, these fluxes become more vigorous and may be comparable to the respective turbulent flows or even to be more powerful. Translated by Vladimir A. Puchkin.     

Transport properties of entrained topographic waves during their interaction with turbulence

In the Boussinesq approximation, topographic waves entrained by a sloping bottom are considered with allowance for turbulent viscosity and diffusion. The mean flows induced by a wave through nonlinearity are determined. The turbulent exchange coefficients are expressed in terms of the density of turbulent energy by using the relations of the semiempirical theory of turbulence. The equation for boundary-layer wave solutions and the equation of turbulent energy balance are solved jointly, which makes it possible to determine the vertical distribution of the density of turbulent energy in the area of the given wave. In the diffusion approximation, the vertical distribution of the concentration of wave-suspended sediments is obtained for the case when the tangential bottom stress exceeds the critical values corresponding to the start of sediment motion.     

Vertical momentum transfer by internal waves when eddy viscosity and diffusion are taken into account

Free internal waves are considered in a Boussinesq approximation in the situation when horizontal eddy viscosity and diffusion in a vertically inhomogeneous flow are taken into account. The dispersion relation and wave damping factor are found in a linear approximation. The Stokes drift velocity is determined in the second order of smallness based on the wave amplitude. It has been indicated that the Stokes drift velocity, transverse with respect to the wave propagation direction, differs from zero if the flow-rate transverse component depends on the vertical coordinate. Vertical momentum fluxes differ from zero and can be comparable with or exceed the corresponding turbulent fluxes if eddy viscosity and diffusion are taken into account.     

Transport Properties of Trapped Topographic Waves

In the Boussinesq approximation, we study weakly nonlinear topographic waves trapped by a flat slope of arbitrary orientation. We compute the mean currents induced by the waves due to the nonlinearity in the quadratic approximation with respect to the wave amplitude in the presence of dissipation of the wave energy into the turbulent motion. In the diffusion approximation, we determine the vertical distribution of the concentration of wave-suspended sediments. It is shown that the consumption of sediments across the isobaths is directed downward along the slope. At the same time, the consumption of sediments along the isobaths has the same direction as the projection of the horizontal wave vector.     

Vertical Transport of Momentum by Internal Waves in a Shear Current

Izvestiya, Atmospheric and Oceanic Physics - Free internal waves are considered in the Boussinesq approximation with account for the rotation of the Earth and a plane–parallel current normal...     

Nonlinear effects in the process of propagation of internal waves with regard for the turbulent viscosity and diffusion

By the method of asymptotic multiscale expansions in the Boussinesq approximation, we study nonlinear effects observed in the process of propagation of internal waves with regard for the turbulent viscosity and diffusion. We determine the decrement of attenuation of waves and the boundary-layer solutions at the bottom and on the free surface. The wave-induced mean current is found in the second order of smallness in the wave steepness. The coefficients of the nonlinear Schr?dinger equation are obtained for the envelope of the wave packet. It is shown that a weakly nonlinear plane wave is stable under longitudinal modulation in the long-wave limit. If the wavelength is smaller than a certain critical value, then the wave is unstable under modulation.