Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell
| Autor: | Yannick Lebranchu, Friedrich H. Busse, Radostin D. Simitev, Emmanuel Plaut |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Journal of Fluid Mechanics. 602:303-326 |
| ISSN: | 1469-7645 0022-1120 |
| DOI: | 10.1017/s0022112008000840 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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