## Vertical Transport of Momentum by the Inertial-Gravity Internal Waves in a Baroclinic Current

*A. A. Slepyshev ^{1, ✉}, D. I. Vorotnikov^{2}*

^{1} Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation

^{2} M.V. Lomonosov Moscow State University, Moscow, Russian Federation

^{✉} e-mail: slep55@mail.ru

### Abstract

When the internal waves break, they are one of the sources of small-scale turbulence. Small-scale turbulence causes the vertical exchange in the ocean. However, internal waves with regard to the Earth rotation in the presence of vertically inhomogeneous two-dimensional current are able to contribute to the vertical transport. Free inertial-gravity internal waves in a baroclinic current in a boundless basin of a constant depth are considered in the Bussinesq approximation. Boundary value problem of linear approximation for the vertical velocity amplitude of internal waves has complex coefficients when current velocity component, which is transversal to the wave propagation direction, depends on the vertical coordinate (taking into account the rotation of the Earth). Eigenfunction and wave frequency are complex, and it is shown that a weak wave damping takes place. Dispersive relation and wave damping decrement are calculated in the linear approximation. At a fixed wave number damping decrement of the second mode is larger (in the absolute value) than the one of the first mode. The equation for vertical velocity amplitude for real profiles of the Brunt – Vaisala frequency and current velocity are numerically solved according to implicit Adams scheme of the third order of accuracy. The dispersive curves of the first two modes do not reach inertial frequency in the low-frequency area due to the effect of critical layers in which wave frequency of the Doppler shift is equal to the inertial one. Termination of the second mode dispersive curves takes place at higher frequency than the one of the first mode. In the second order of the wave amplitude the Stokes drift speed is determined. It is shown that the Stokes drift speed, which is transversal to the wave propagation direction, differs from zero if the transversal component of current velocity depends on the vertical coordinate. In this case, the Stokes drift speed in the second mode is lower than in the first mode only in the pycnocline, outside the pycnocline their values are comparable in absolute value. The longitudinal component of the Stokes drift velocity of 15-min second mode internal waves observed in the field experiment during the 44^{th} voyage of R/V “Mikhail Lomonosov” on the northwestern shelf of the Black Sea is by an order of magnitude greater than the transversal one. Vertical wave fluxes of the momentum also differ from zero and can be either comparable with the corresponding turbulent fluxes or exceed them.

### Keywords

internal waves, turbulence, momentum fluxes, Stokes drift, critical layer

### For citation

Slepyshev, A.A. and Vorotnikov, D.I., 2017. Vertical Transport of Momentum by the Inertial-Gravity Internal Waves in a Baroclinic Current. *Physical Oceanography*, (4), pp. 3-15. doi:10.22449/1573-160X-2017-4-3-15

### DOI

10.22449/1573-160X-2017-4-3-15

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