Abstract.
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 \(\nu\) ) within such a region. To establish this result rigorously, as a first step we here show that a boundary layer corresponding to the PB theory exists and is unique for the circular eddy under relatively small perturbations of the Euler limit wall velocity.
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Received: January 28; revised: April 7, 1999
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Kim, SC. On Prandtl-Batchelor theory of a cylindrical eddy: Existence and uniqueness. Z. angew. Math. Phys. 51, 674–686 (2000). https://doi.org/10.1007/PL00001514
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DOI: https://doi.org/10.1007/PL00001514