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

Nonlinear effects in the process of propagation of internal waves with regard for the turbulent... 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 Schrödinger 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Oceanography Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2009 by Springer Science+Business Media, Inc.
Subject
Earth Sciences; Oceanography; Remote Sensing/Photogrammetry; Atmospheric Sciences; Climate Change; Environmental Physics
ISSN
0928-5105
eISSN
0928-5105
D.O.I.
10.1007/s11110-010-9053-7
Publisher site
See Article on Publisher Site

Abstract

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 Schrödinger 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.

Journal

Physical OceanographySpringer Journals

Published: Mar 27, 2010

References

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