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Interscale transfer in two-dimensional compact vortices

Published online by Cambridge University Press:  10 March 2000

GIANNI PEDRIZZETTI  and
J. C. VASSILICOS
GIANNI PEDRIZZETTI
Affiliation:
Dipartimento Ingegneria Civile, Università di Trieste, P.le Europa 1, 34127 Trieste, Italy; e-mail: [email protected]
J. C. VASSILICOS
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK; e-mail: [email protected]
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Abstract

The property of transfer between different scales of motion in evolving two-dimensional compact vortices is studied here, and a general mathematical framework is developed to describe the transfer between scales inside compact structures. This new approach is applied to the case of an axisymmetric advection which represents the leading-order (large time) approximation for Lundgren's family of two-dimensional vortices. It is also generalized to passive scalar advection by non-axisymmetric velocity fields. It is shown that scale interactions generated by an axisymmetric advection are essentially local and dominated by distant triadic interactions: in the case of an evolving spiral vortex sheet this result is confirmed even when non-axisymmetric corrections are included. A physical interpretation of the results is given, which can be summarized by saying that locality of scale interactions is caused by the uniformity of shear at a given scale and is therefore increasingly natural at small lengthscales. Local interactions are shown to arise in axisymmetric advection but to be uncommon in non-axisymmetric advection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 406 , 10 March 2000 , pp. 109 - 129
Copyright
© 2000 Cambridge University Press

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