aDepartment of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
bAustralian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems, University of New South Wales, Sydney, Australia
Abstract:
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.