Cauchy integral formula for generalized analytic functions in hydrodynamics

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Abstract

It is shown that for several classes of generalized analytic functions arising in linearized equations of hydrodynamics and magnetohydrodynamics, the Cauchy integral formulae follow from the one for generalized holomorphic vectors in a uniform fashion. If hydrodynamic fields (velocity, pressure and vorticity) admit representations in terms of corresponding generalized analytic functions, those representations and the Cauchy integral formulae form two essential parts of the generalized analytic function approach, which readily yields either closed-form solutions or boundary integral equations. This approach is demonstrated for problems of axisymmetric and asymmetric Stokes flows, two-phase axisymmetric Stokes flows, two-dimensional and axisymmetric Oseen flows.

Original languageEnglish
Pages (from-to)3745-3764
Number of pages20
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume468
Issue number2148
DOIs
StatePublished - 8 Dec 2012

Keywords

  • Cauchy integral formula
  • Generalized analytic function
  • Oseen flow
  • Stokes flow

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