Doubly periodic and multiple pole solutions of the sinh-Poisson equation: application of reciprocal transformations in subsonic gas dynamics
Doubly periodic and multiple pole solutions of the sinh-Poisson equation: application of reciprocal transformations in subsonic gas dynamics
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DOI：
10.1016/j.cam.2004.12.042
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发表时间：
2006-06
影响因子：
2.4
通讯作者：
K. Chow;C. Mak;C. Rogers;W. Schief
中科院分区：
文献类型：
--
作者：
K. Chow;C. Mak;C. Rogers;W. Schief
与Sinh-Poisson方程相关的涡型作为Navier-Stokes方程的弛豫态以一种引人注目的方式出现。利用Hirota双线性算子形式和波数合并现象，得到了Sinh-Poisson方程的双周期解和多极解。然后说明了如何将气体动力学的多参数倒易变换应用于Sinh-Poisson方程的种子双周期解，以产生在广义Kármán-Tsien气体的亚音速流动中有效的相关周期涡旋结构。
Vortex patterns associated with the sinh-Poisson equation arise in a remarkable manner as relaxation states of the Navier–Stokes equations. Here, doubly periodic and multiple-pole solutions of the sinh-Poisson equation are generated via the Hirota bilinear operator formalism and exploitation of the phenomenon of coalescence of wave numbers. It is then shown how the multi-parameter reciprocal transformations of gas dynamics may be applied to a seed doubly periodic solution of the sinh-Poisson equation to generate associated periodic vortex structures valid in the subsonic flow of a generalized Kármán–Tsien gas.