The axisymmetric Prandtl-Batchelor eddy behind a circular disc in a uniform stream

The axisymmetric Prandtl-Batchelor eddy behind a circular disc in a uniform stream

J.Fluid.Mech. 377, 253-266, 1998

Analytical support is given to Fornberg's numerical evidence that the steady axially symmetric flow of a uniform stream past a bluff body has a wake eddy which tends towards a large Hill's spherical vortex as the Reynolds number tends to infinity. The viscous boundary layer around the eddy resembles that around a liquid drop rising in a liquid, especially if the body is a circular disc, so that the boundary layer on it does not separate. This makes it possible to show that if the first-order perturbation of the eddy shape from a sphere is small then the eddy diameter is of order $R^{1/5}$ times the disc diameter, where $R$ is the Reynolds number based on the disc diameter. Previous authors had suggested $R^{1/3}$ and $\ln R$, but they appear to have made unjustified assumptions.

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