Vertical Momentum Transfer Due to Internal Waves

A. A. Slepyshev✉, A. V. Nosova

Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

✉ e-mail: slep55@mail.ru

Abstract

Purpose. The work aims to study the vertical momentum transfer by internal waves at the exit of the Strait of Gibraltar into the Mediterranean Sea, accounting for turbulent viscosity and diffusion.

Methods and Results. In contrast to the traditional approach relating vertical momentum transfer to small-scale turbulence, the present study examines the wave transport mechanism. The wave field is described using classical hydrodynamic equations for a stratified incompressible fluid with shear flow, incorporating turbulent viscosity and diffusion. The boundary value problem for the vertical velocity amplitude of internal waves, which conditions the mode structure, is solved numerically. In the linear approximation, the complex nature of the coefficients results in a complex solution, leading to a non-zero vertical wave momentum flux. The impact of horizontal turbulent viscosity and diffusion on this flux is investigated. Three models are compared: the first one – with constant exchange coefficients (basic case), the second – with exchange coefficients depending on phenomenon scale according to the “4/3” law, and the third – with coefficients of horizontal exchange taking into account stratification. It is shown that when the dependence of exchange coefficients on the phenomenon scale according to the “4/3” law is taken into account, the momentum flux is higher in magnitude than that with constant coefficients, but lower than the fluxes taking into account stratification. The same pattern holds for the vertical component of the Stokes drift velocity. The choice of exchange coefficients has virtually no effect on the horizontal component of the Stokes drift velocity.

Conclusions. The dispersion curves of internal waves are independent of the choice of exchange coefficients. However, the wave attenuation decrement is sensitive to this choice: it is higher in magnitude when the exchange coefficients depend on the phenomenon scale according to the “4/3” law compared to the case of constant exchange coefficients, and even higher in absolute value when stratification is taken into account. The same pattern holds true for the vertical wave momentum flux.

Keywords

internal waves, wave momentum flux, Stokes drift, turbulent viscosity, turbulent diffusion

Acknowledgements

This study was conducted under the state assignment of FSBSI FRC MHI (FNNN-2021-0004), titled “Fundamental research of oceanographic processes which determine the state and evolution of marine environment under the impact of natural and anthropogenic factors based on the observation and modeling methods”.

Original russian text

Original Russian Text © A. A. Slepyshev, A. V. Nosova, 2025, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 41, Iss. 5, pp. 573-585 (2025)

For citation

Slepyshev, A.A. and Nosova, A.V., 2025. Vertical Momentum Transfer Due to Internal Waves. Physical Oceanography, 32(5), pp. 589-600.

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