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Internal gravity waves in shear flows at large Reynolds number

Published online by Cambridge University Press:  21 April 2006

Cornelis A. Van Duin
Affiliation:
Division of Geophysics, Royal Netherlands Meteorological Institute. 3730 AE De Bilt, The Netherlands
Hennie Kelder
Affiliation:
Division of Geophysics, Royal Netherlands Meteorological Institute. 3730 AE De Bilt, The Netherlands

Abstract

The effects of viscosity and heat conduction on the propagation of internal gravity waves are examined. These waves propagate in a stably stratified, parallel shear flow with one critical level. The Boussinesq approximation is adopted. For large Reynolds number the governing sixth-order differential equation is solved by analytical methods. In the limit of large Reynolds number it is found that the reflection and transmission coefficients for a wave incident in a viscous fluid are the same as in the inviscid case. Hence over-reflection can also occur in a viscous fluid. For the perturbed velocity components at the critical level, asymptotic expressions are derived. The results we obtain are valid for smooth, but otherwise arbitrary, shear-flow and density profiles.

Type
Research Article
Copyright
© 1986 Cambridge University Press

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