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Impulse formulation of the Euler equations: general properties and numerical methods

Published online by Cambridge University Press:  25 July 1999

GIOVANNI RUSSO  and
PETER SMEREKA
GIOVANNI RUSSO
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università dell'Aquila, Via Vetoio, 67010 L'Aquila, Italy
PETER SMEREKA
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
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Abstract

The gauge freedom of the incompressible Euler equations is explored. We present various forms of the Euler equations written in terms of the impulse density. It is shown that these various forms are related by a gauge transformation. We devise a numerical method to solve the impulse form of the Euler equations in a variety of gauges. The numerical scheme is implemented both in two and three space dimensions. Numerical results are presented showing that the impulse density tends to concentrate on sheets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 391 , 25 July 1999 , pp. 189 - 209
Copyright
© 1999 Cambridge University Press

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