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A model of turbulent mixing across a density interface including the effect of rotation

Published online by Cambridge University Press:  26 April 2006

Mathieu Mory
Mathieu Mory
Affiliation:
Institut de Mécanique de Grenoble, Domaine Universitaire, BP 53X, 38041 Grenoble Cédex, France
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Abstract

A new theoretical approach is presented, which determines the entrainment laws with and without background rotation in a two-layer stratified fluid with one layer stirred by turbulent motions. The model gives the entrainment coefficient E as a function of the local turbulent Richardson number Ri = g′l/u2, the Rossby number Ro = u/fl and the Péelet number Pe = ul/κ. The following entrainment laws are obtained: (i) without rotation and for a high Péclet number: $E \propto Ri^{-\frac{3}{2}}$; (ii) without rotation and for a low to moderate Péclet number: $E \propto Pe^{-\frac{1}{3}}Ri^{-1}$ (iii) with rotation and for a high Péclet number: E ∝ RoRi−l. These entrainment laws are consistent with experiments for the three different cases. The model relies to a great extent on the spectral distribution of interface oscillations measured in experiments. Comparison is made with experiments and with earlier models of entrainment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 193 - 207
Copyright
© 1991 Cambridge University Press

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