论文标题
关于Burgers-Hilbert方程的涡流前沿的近似
On the approximation of vorticity fronts by the Burgers-Hilbert equation
论文作者
论文摘要
本文证明，通过Biello and Hunter（2010）衍生出正式的渐近扩展，Burgers-Hilbert方程在三维不可压缩的Euler方程中的小斜率涡流方程式的运动近似。该证明使用修改的能量法来证明Euler方程中涡度前沿和Burgers-Hilbert方程的轮廓动力学方程都通过相同的立方非线性渐近方程近似。还得出了Euler涡度前沿的轮廓动力学方程。
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.
