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Wave boundary layers in a stratified fluid

Published online by Cambridge University Press:  07 November 2017

G. M. Reznik Open the ORCID record for G. M. Reznik [Opens in a new window]
G. M. Reznik*
Affiliation:
Shirshov Institute of Oceanology, Russian Academy of Sciences, 36, Nakhimovskiy Prospekt, 117997, Moscow, Russia
*
†Email address for correspondence: [email protected]
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Abstract

We study so-called wave boundary layers (BLs) arising in a stably stratified fluid at large times. The BL is a narrow domain near the surface and/or bottom of the fluid; with increasing time, gradients of buoyancy and horizontal velocity in the BL grow sharply and the BL thickness tends to zero. The non-stationary BL can arise both as a result of linear evolution of the initial perturbation and under the action of an external force (tangential stress exerted on the fluid surface in our case). We analyse both the variants and find that the ‘forced’ BLs are much more intense than the ‘free’ ones. In the ‘free’ BLs all fields are bounded and the gradients of buoyancy and horizontal velocity grow linearly in time, whereas in the ‘forced’ BL only the vertical velocity is bounded and the buoyancy and horizontal velocity grow linearly in time. As to the gradients in the ‘forced’ BL, the vertical velocity gradient grows in time linearly and the gradients of buoyancy and horizontal velocity grow quadratically. In both of the cases we determine exact solutions in the form of expansions in the vertical wave modes and find asymptotic solutions valid at large times. The comparison between them shows that the asymptotic solutions approximate the exact ones fairly well even for moderate times.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 833 , 25 December 2017 , pp. 512 - 537
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Copyright
© 2017 Cambridge University Press 

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