On Prandtl-Batchelor theory of a cylindrical eddy: Existence and uniqueness

초록

For a steady laminar two-dimensional flow, Prandtl and Batchelor proposed a property in the case of a region of nested closed streamlines. This Prandtl-Batchelor(PB) theory claims the constancy of the vorticity in the limit of infinite Reynolds number R ( or vanishing viscosity v ) within such a region. To establish this result rigorously, as a first step we here show that a boundary layer corresponding to the PE theory exists and is unique for the circular eddy under relatively small perturbations of the Euler limit wall velocity. Mathematics Subject Classification (2000). 76C05, 76D05, 76D10.

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