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The rollup of a vortex layer near a wall

Published online by Cambridge University Press:  26 April 2006

Javier Jiménez  and
Paolo Orlandi
Javier Jiménez
Affiliation:
School of Aeronautics, U. Politécnica, Pl. Cardenal Cisneros 3, 28040 Madrid, Spain Centre for Turbulence Research, Standford University, CA 94305, USA and NASA Ames Research Centre, CA 94035, USA
Paolo Orlandi
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università ‘La Sapienza’, Via Eudossiana 16, 00184, Roma, Italy Centre for Turbulence Research, Standford University, CA 94305, USA and NASA Ames Research Centre, CA 94035, USA
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Abstract

The behaviour of an inviscid vortex layer of non-zero thickness near a wall is studied, both through direct numerical simulation of the two-dimensional vorticity equation at high Reynolds numbers, and using an approximate ordinary nonlinear integro-differential equation which is satisfied in the limit of a thin layer under long-wavelength perturbations. For appropriate initial conditions the layer rolls up and breaks into compact vortices which move along the wall at constant speed. Because of the effect of the wall, they correspond to equilibrium counter-rotating vortex dipoles. This breakup can be related to the disintegration of the initial conditions of the approximate nonlinear dispersive equation into solitary waves. The study is motivated by the formation of longitudinal vortices from vortex sheets in the wall region of a turbulent channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 297 - 313
Copyright
© 1993 Cambridge University Press

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