Vertical Transfer of Momentum by Internal Waves in the Western Part of the Mediterranean Sea

A. A. Slepyshev✉, A. V. Nosova

Marine Hydrophysical Institute of RAS, Sevastopol, Russian Federation

✉ e-mail: slep55@mail.ru

Abstract

Purpose. The work is aimed at studying both the momentum vertical transfer by internal waves with the regard for the Earth rotation and the shear current in the western part of the Mediterranean Sea, and the influence of turbulent viscosity and diffusion upon the indicated wave fluxes and the Stokes drift.

Methods and Results. To solve the initial system of the hydrodynamics nonlinear equations, a weakly nonlinear approach was used. In the first order of smallness in the wave amplitude, the boundary problem for the vertical velocity amplitude was solved; in the second order in the wave amplitude, the nonlinear effects, namely the Stokes drift and the vertical wave momentum fluxes, were investigated. The indicated boundary problem was solved in two ways: by the perturbation method applied earlier and by the numerical one by the implicit Adams scheme of the third order of accuracy. The perturbation method assumes expansion of the solution and the wave frequency in a series by a small parameter proportional to the horizontal turbulent viscosity. The results obtained by the perturbation and numerical methods were compared. Coincidence of the results of calculating the dispersion curves by both methods is shown. However, for the wave damping decrement, the perturbation method yields the overestimated values, at that for the second mode the values are higher than those for the first one. The vertical wave momentum fluxes are nonzero, and theperturbation method yields the overestimated values for the flux uw. The vertical wave momentum flux vw is practically independent of turbulent viscosity and diffusion, and both methods give the identical results for it. The velocity component of the Stokes drift along the wave propagation direction is also insensitive to turbulent viscosity and diffusion, whereas the transverse component equals zero in the absence of turbulent viscosity and diffusion.

Conclusions. The perturbation method provides the overestimated values of the wave damping decrements, the wave momentum flux uw and the transverse component of the Stokes drift velocity. The horizontal turbulent viscosity and diffusion exert practically no effect upon the wave momentum flux vw and the longitudinal component of the Stokes drift velocity.

Keywords

internal waves, wave momentum flux, Stokes drift

Acknowledgements

The study was carried out within the framework of the state assignment on theme No. 0555-2021-0004.

Original russian text

Original Russian Text © A. A. Slepyshev, A. V. Nosova, 2022, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 38, Iss. 4, pp. 358-371 (2022)

For citation

Slepyshev, A.A. and Nosova, A.V., 2022. Vertical Transfer of Momentum by Internal Waves in the Western Part of the Mediterranean Sea. Physical Oceanography, 29(4), pp. 334-346. doi:10.22449/1573-160X-2022-4-334-346

DOI

10.22449/1573-160X-2022-4-334-346

References

  1. Bulatov, V.V. and Vladimirov, Yu.V., 2015. Waves in Stratified Medium. Moscow: Nauka, 735 p. (in Russian).
  2. Korotaev, G.K. and Panteleev, N.A., 1977. Experimental Studies of Hydrodynamic Instability in the Ocean. Okeanologiya, 17(6), pp. 941-953 (in Russian).
  3. Wunsch, C. and Ferrari, R., 2004. Vertical Mixing, Energy, and the General Circulation of the Ocean. Annual Review of Fluid Mechanics, 36, pp. 281-314. doi:10.1146/annurev.fluid.36.050802.122121
  4. Samodurov, A.S., Lubitsky, A.A. and Panteleev, N.A., 1995. Contribution of Breaking Internal Waves to Structure Formation, Energy Dissipation, and Vertical Diffusion in the Ocean. Physical Oceanography, 6(3), pp. 177-190. doi:10.1007/BF02197516
  5. Korotaev, G.K. and Panteleev, N.A., 1977. Hydrodynamical Instability of Internal Waves with Nonstationary Shear. Izvestiya Akademii Nauk SSSR. Fizika Atmosfery i Okeana, 13(10), pp. 1044-1054 (in Russian).
  6. Podymov, O.I., Zatsepin, A.G. and Ostrovsky, A.G., 2017. Vertical Turbulent Exchange in the Black Sea Pycnocline and Its Relation to Water Dynamics. Oceanology, 57(4), pp. 492- 504. doi:10.1134/S0001437017040142
  7. Panteleev, N.A., Shcherbakov, A.N. and Shcherbakova, E.N., 1989. The Observation of the Hydrodynamical Instability in the Ocean. Izvestiya Akademii Nauk SSSR. Fizika Atmosfery i Okeana, 25(6), pp. 616-626 (in Russian).
  8. LeBlond, P.H. and Mysak, L.A., 1978. Waves in the Ocean. Amsterdam–Oxford–New York: Elsevier Scientific Publishing Company, 602 p.
  9. LeBlond, P.H., 1966. On the Damping of Internal Gravity Waves in a Continuously Stratified Ocean. Journal of Fluid Mechanics, 25(1), pp. 121-142. doi:10.1017/S0022112066000089
  10. Ostrovsky, L.A. and Soustova, I.A., 1979. The Upper Mixed Layer of the Ocean as an Energy Sink of Internal Waves. Okeanologiya, 19(6), pp. 973-981 (in Russian).
  11. Slepyshev, A.A., 2016. Vertical Momentum Transfer by Internal Waves when Eddy Viscosity and Diffusion are Taken into Account. Izvestiya, Atmospheric and Oceanic Physics, 52(3), pp. 301-308. doi:10.1134/S0001433816030117
  12. Slepyshev, A.A. and Nosova, A.V., 2020. Generation of Vertical Fine Structure by the Internal Waves with the Regard for Turbulent Viscosity and Diffusion. Physical Oceanography, 27(1), pp. 3-17. doi:10.22449/1573-160X-2020-1-3-17
  13. Ankudinov, N.O. and Slepyshev, A.A., 2021. Vertical Momentum Transfer Induced by Internal Waves in a Two-Dimensional Flow. Fluid Dynamics, 56(3), pp. 343-352. doi:10.1134/S0015462821030022
  14. Vorotnikov, D.I. and Slepyshev, A.A., 2018. Vertical Momentum Fluxes Induced by Weakly Nonlinear Internal Waves on the Shelf. Fluid Dynamics, 53(1), pp. 21-33. doi:10.1134/S0015462818010160
  15. Longuet-Higgins, M.S., 1969. On the Transport of Mass by Time-Varying Ocean Currents. Deep Sea Research and Oceanographic Abstracts, 16(5), pp. 431-447. doi:10.1016/0011- 7471(69)90031-X
  16. Watson, G., 1994. Internal Waves in a Stratified Shear Flow: The Strait of Gibraltar. Journal of Physical Oceanography, 24(2), pp. 509-517. doi:10.1175/1520- 0485(1994)024<0509:IWIASS>2.0.CO;2
  17. Bowden, K.F., 1983. Physical Oceanography of Coastal Waters. New York: Halsted Press, 302 p.
  18. Ivanov, V.A., Samodurov, A.S., Chukharev, A.M. and Nosova, A.V., 2008. Intensification of Vertical Turbulent Exchange in the Vicinity of the Interface between the Shelf and the Continental Slope in the Black Sea. Reports of the National Academy of Sciences of Ukraine, (6), pp. 108-112 (in Russian).
  19. Samodurov, A.S., 2016. Complimentarity of Different Approaches for Assessing Vertical Turbulent Exchange Intensity in Natural Stratified Basins. Physical Oceanography, (6), pp. 32-42. doi:10.22449/1573-160X-2016-6-32-42

Download the article (PDF)