Asymptotic solution for high vorticity regions in incompressible 3D Euler equations

Abstract

Incompressible 3D 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 pseudo-spectral method in anisotropic grids of up to 972 x 2048 x 4096.

arXiv comment13 pages, 4 figures

References in corpus (2)

• Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
• Development of high vorticity structures in incompressible 3D Euler equations

Cited by in corpus (11)

• Chaotic blowup in the 3D incompressible Euler equations on a logarithmic lattice
• Fluid dynamics on logarithmic lattices
• Development of high vorticity structures and geometrical properties of the vortex line representation
• Exact Time-Dependent Solution to the Three-Dimensional Euler- Helmholtz and Riemann-Hopf Equations for Vortex Flow of a Compressible Medium and the Sixth Millennium Prize Problem
• Slipping flows and their breaking
• Compressible vortex structures and their role in the onset of hydrodynamic turbulence
• Lagrangian dynamics and regularity of the spin Euler equation
• Notes about collapse in magnetohydrodynamics
• Statistical properties of the velocity field for the 3D hydrodynamic turbulence onset
• Stability of tangential discontinuity for the vortex pancakes
• A filamentary cascade model of the inertial range