Plaut, E., Lebranchu, Y., Simitev, R. and Busse, F.H. (2008) Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell. Journal of Fluid Mechanics, 602, pp. 303-326. (doi: 10.1017/S0022112008000840)
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Abstract
A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Simitev, Professor Radostin |
Authors: | Plaut, E., Lebranchu, Y., Simitev, R., and Busse, F.H. |
Subjects: | Q Science > QC Physics |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Fluid Mechanics |
Publisher: | Cambridge University Press |
ISSN: | 0022-1120 |
ISSN (Online): | 1469-7645 |
Published Online: | 25 April 2008 |
Copyright Holders: | Copyright © 2008 Cambridge University Press |
First Published: | First published in Journal of Fluid Mechanics 602:303-326 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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