On the approximation of vorticity fronts by the Burgers-Hilbert equation
Analysis of PDEs
2021-02-22 v2
Abstract
This paper proves that the motion of small-slope vorticity fronts in the two-dimensional incompressible Euler equations is approximated on cubically nonlinear timescales by a Burgers-Hilbert equation derived by Biello and Hunter (2010) using formal asymptotic expansions. The proof uses a modified energy method to show that the contour dynamics equations for vorticity fronts in the Euler equations and the Burgers-Hilbert equation are both approximated by the same cubically nonlinear asymptotic equation. The contour dynamics equations for Euler vorticity fronts are also derived.
Keywords
Cite
@article{arxiv.2006.08163,
title = {On the approximation of vorticity fronts by the Burgers-Hilbert equation},
author = {John K. Hunter and Ryan C. Moreno-Vasquez and Jingyang Shu and Qingtian Zhang},
journal= {arXiv preprint arXiv:2006.08163},
year = {2021}
}
Comments
29 pages, 1 figure