Shape calculus for vortex patch equilibria and its application to lattice configurations

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)86-100
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume332
DOIs
Publication statusPublished - 2018 Apr
Externally publishedYes

Keywords

  • Free-boundary problem
  • Lattice
  • Shape derivative
  • Vortex equilibria
  • Vortex patch

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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