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The critical layer for internal gravity waves in a shear flow

Published online by Cambridge University Press:  28 March 2006

John R. Booker and
Francis P. Bretherton
John R. Booker
Affiliation:
Institute of Geophysics and Planetary Physics, La Jolla, California
Francis P. Bretherton
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Internal gravity waves of small amplitude propagate in a Boussinesq inviscid, adiabatic liquid in which the mean horizontal velocity U(z) depends on height z only. If the Richardson number R is everywhere larger than 1/4, the waves are attenuated by a factor $\exp\{-2\pi(R - \frac{1}{4})^{\frac{1}{2}}\}$ as they pass through a critical level at which U is equal to the horizontal phase speed, and momentum is transferred to the mean flow there. This effect is considered in relation to lee waves in the airflow over a mountain, and in relation to transient localized disturbances. It is significant in considering the propagation of gravity waves from the troposphere to the ionosphere, and possibly in transferring horizontal momentum into the deep ocean without substantial mixing.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 3 , 24 February 1967, pp. 513 - 539
Copyright
© 1967 Cambridge University Press

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