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arXiv · 2006.08163

On the approximation of vorticity fronts by the Burgers-Hilbert equation

John K. Hunter·Ryan C. Moreno-Vasquez·Jingyang Shu·Qingtian Zhang
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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.

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John K. Hunter, Ryan C. Moreno-Vasquez, Jingyang Shu, Qingtian Zhang. 2021-02-19. On the approximation of vorticity fronts by the Burgers-Hilbert equation. https://arxiv.org/abs/2006.08163

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