Shape calculus for vortex patch equilibria and its application to lattice configurations
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摘要
A new shape derivative formula for singular contour integrals with logarithmic kernels is proposed. This formula yields a simple numerical scheme for computing vortex patch equilibria. Owing to its simplicity, any steady configuration of point vortices can be extended to that of vortex patches. As a test problem, a doubly periodic array of vortex patches is considered to show the efficiency of the new formula. Several non-trivial families of stationary vortex patch lattices are also presented.
论文关键词:76-06,76B47,76M25,35R35,Free-boundary problem,Shape derivative,Vortex patch,Vortex equilibria,Lattice
论文评审过程:Received 8 December 2016, Revised 21 September 2017, Accepted 16 October 2017, Available online 26 October 2017, Version of Record 3 November 2017.
论文官网地址:https://doi.org/10.1016/j.cam.2017.10.023