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Internal gravity waves: critical layer absorption in a rotating fluid

Published online by Cambridge University Press:  29 March 2006

R. Grimshaw
R. Grimshaw
Affiliation:
Mathematics Department, University of Melbourne, Parkville, Victoria 3052, Australia
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Abstract

The propagation of internal gravity waves in a shear flow in a rotating fluid is examined for the case when the rotation vector is inclined to the vertical. It is shown that internal gravity waves approaching a critical level, where ω*, the Doppler-shifted frequency, equals 2ΩV, the vertical component of the Coriolis parameter, will be either transmitted or absorbed according as \[ W_g\omega^{*}2\Omega_V\{m(U_z + 2\Omega_H)-lV_z\}\lessgtr 0; \] here Wg is the vertical group velocity, 2ΩH is the horizontal component of the Coriolis parameter, l and m are the easterly and northerly wavenumber components, and Uz and Vz are the shear rates of the easterly and northerly components of the mean flow. Between critical levels, wave action flux is conserved. However, for a wave absorbed at a critical level, the wave action flux is attenuated by a factor exp { − 2π|m(Uz + 2ΩH) − lVz]/(lUz + mVz)|}. The phenomenon is also analysed using a WKBJ approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 2 , 29 July 1975 , pp. 287 - 304
Copyright
© 1975 Cambridge University Press

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References

Acheson, D. J. 1972 J. Fluid Mech. 53, 401–415.
Acheson, D. J. 1973 J. Fluid Mech. 58, 27–37.
Booker, J. R. & Bretherton, F. P. 1967 J. Fluid Mech. 27, 513–539.
Bretherton, F. P. 1966 Quart. J. Roy. Met. Soc. 92, 466–480.
Bretherton, F. P. & Garrett, C. J. R. 1968 Proc. Roy. Soc. A 302, 529–554.
Frankignoul, C. J. 1970 Tellus, 22, 194–203.
Frankignoul, C. J. 1972 Mém. Soc. Roy. Sci. Liege 2 (6), 51–58.
Garrett, C. J. R. 1968 J. Fluid Mech. 34, 711–720.
Grimshaw, R. 1972 J. Fluid Mech. 54, 193–207.
Grimshaw, R. 1974a Geophys. Fluid Dyn. 6, 131–148.
Grimshaw, R. 1974b School Math. Sci., University of Melbourne, Resp. Rep. no. 20.
Jones, W. L. 1967 J. Fluid Mech. 30, 439–448.
Lewis, R. M. 1965 Arch. Rat. Mech. Anal. 20, 191–250.
Mckenzie, J. F. 1973 J. Fluid Mech. 58, 709–726.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Rudraiah, N. & Venkatachalappa, M. 1972a J. Fluid Mech. 52, 193–206.
Rudraiah, N. & Venkatachalappa, M. 1972b J. Fluid Mech. 54, 217–240.