Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

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)

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
• 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