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Rotating free-shear flows. Part 2. Numerical simulations

Published online by Cambridge University Press:  26 April 2006

Olivier Métais ,
Carlos Flores ,
Shinichiro Yanase ,
James J. Riley  and
Marcel Lesieur
Olivier Métais
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels de Grenoble, URA CNRS 1509, Institut de Mécanique de Grenoble, Institut National Polytechnique et Université Joseph Fourier, Grenoble, BP 53, 38041 Grenoble Cédex 9, France
Carlos Flores
Affiliation:
Departemento de Oceanografia- CFE, Mexico, DF, 03810, Mexico
Shinichiro Yanase
Affiliation:
Engineering Mathematics, Faculty of Engineering, Okayama University, Tsushimanaka, Okayama 700, Japan
James J. Riley
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Marcel Lesieur
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels de Grenoble, URA CNRS 1509, Institut de Mécanique de Grenoble, Institut National Polytechnique et Université Joseph Fourier, Grenoble, BP 53, 38041 Grenoble Cédex 9, France
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Abstract

The three-dimensional dynamics of the coherent vortices in periodic planar mixing layers and in wakes subjected to solid-body rotation of axis parallel to the basic vorticity are investigated through direct (DNS) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturbation being either quasi-two-dimensional (forced transition) or three-dimensional (natural transition). For an initial Rossby number Ro(i), based on the vorticity at the inflexion point, of small modulus, the effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor–Proudman theorem. In this case, the longitudinal vortices found in forced transition without rotation are suppressed.

It is shown that, in a cyclonic mixing layer, rotation inhibits the growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case for |Ro(i)| ≤ 1. At moderate anticyclonic rotation rates (Ro(i) < −1), the flow is strongly destabilized. Maximum destabilization is achieved for |Ro(i) ≈ 2.5, in good agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alternate absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin–Helmholtz vortices have been suppressed. The background velocity profile exhibits a long range of nearly constant shear whose vorticity exactly compensates the solid-body rotation vorticity. This is in agreement with the phenomenological theory proposed by Lesieur, Yanase & Métais (1991). As expected, the stretching is more efficient in the LES than in the DNS.

A rotating wake has one side cyclonic and the other anticyclonic. For |Ro(i)| ≤ 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (|Ro(i)| > 1), the cyclonic side is composed of Kármán vortices without longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with intense longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximum destabilization is still observed for |Ro(i)| ≈ 2.5, as in the linear theory.

The paper also analyses the effect of rotation on the energy transfers between the mean flow and the two-dimensional and three-dimensional components of the field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 293 , 25 June 1995 , pp. 47 - 80
Copyright
© 1995 Cambridge University Press

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