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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  and
Hennie Kelder
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
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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
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 293 - 306
Copyright
© 1986 Cambridge University Press

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