A family of axisymmetric vortex flows with a surface discontinuity of the bernoulli constant

Abstract

One-parameter class of steady axisymmetric vortex flows of incompressible inviscid fluid with vorticity satisfying the Prandtl— Batchelor condition is considered. The Bernoulli constant becomes discontinuous and changes by a given quantity at the surface separating the external potential stream from the vortex flow region. Determination of the stream function is reduced to solving a system of two nonlinear integral equations for the boundary of the vortex flow region and of intensity of the vortex sheet contained in it. Results of numerical calculations are presented.