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Fluid Dynamics

, Volume 53, Issue 1, pp 21–33 | Cite as

Vertical Momentum Fluxes Induced by Weakly Nonlinear Internal Waves on the Shelf

  • D. I. Vorotnikov
  • A. A. Slepyshev
Article

Abstract

Free inertia-gravity internal waves in a two-dimensional stratified flow of an ideal fluid with a vertical velocity shear are considered in the Boussinesq approximation. The boundary-value problem for the amplitude of the vertical velocity of internal waves has complex coefficients; therefore, the wave frequency has an imaginary correction and the eigenfunction is complex. It is shown that the wave is weakly damped, the vertical wave momentum fluxes being nonzero and can be greater than the turbulent fluxes. The Stokes drift velocity component transverse to the direction of wave propagation is nonzero and less than the longitudinal component by an order of magnitude. The dispersion curves of the first two modes are cut off in the low-frequency domain due to the influence of critical layers in which the wave frequency taken with the Doppler shift is equal to the inertial frequency.

Key words

wave momentum fluxes Stokes drift critical layers 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Physics DepartmentLomonosov Moscow State UniversityMoscowRussia
  2. 2.Marine Hydrophysical Institute of the Russian Academy of SciencesSevastopolRussia
  3. 3.Branch of Lomonosov Moscow State UniversitySevastopolRussia

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