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

  • D. S. Agafontsev (a1) (a2), E. A. Kuznetsov (a2) (a3) and A. A. Mailybaev (a4)
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 $972\times 2048\times 4096$ .

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Email address for correspondence: alexei@impa.br
References
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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