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Asymptotic solution for high-vorticity regions in incompressible three-dimensional Euler equations

Published online by Cambridge University Press:  17 January 2017

D. S. Agafontsev ,
E. A. Kuznetsov  and
A. A. Mailybaev
D. S. Agafontsev
Affiliation:
P. P. Shirshov Institute of Oceanology, Moscow 117218, Russia Novosibirsk State University, Novosibirsk 630090, Russia
E. A. Kuznetsov
Affiliation:
Novosibirsk State University, Novosibirsk 630090, Russia P. N. Lebedev Physical Institute, Moscow 119991, Russia
A. A. Mailybaev*
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada – IMPA, Rio de Janeiro 22460-320, Brazil
*
†Email address for correspondence: alexei@impa.br
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Abstract

Incompressible three-dimensional Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work, we propose an exact solution of the Euler equations for the asymptotic pancake evolution. This solution combines a shear flow aligned with an asymmetric straining flow, and is characterized by a single asymmetry parameter and an arbitrary transversal vorticity profile. The analysis is based on detailed comparison with numerical simulations performed using a pseudospectral method in anisotropic grids of up to $972\times 2048\times 4096$.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , R1
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Copyright
© 2017 Cambridge University Press 

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