The ANZIAM Journal

Research Article

Steady Prandtl-Batchelor flows past a circular cylinder

G. C. Hockinga1

a1 Mathematics & Statistics, Murdoch University, Murdoch, WA 6150, Australia; e-mail:


The high Reynolds number flow past a circular cylinder with a trailing wake region is considered when the wake region is bounded and contains uniform vorticity. The formulation allows only for a single vortex pair trapped behind the cylinder, but calculates solutions over a range of values of vorticity. The separation point and length of the region are determined as outputs. It was found that using this numerical method there is an upper bound on the vorticity for which solutions can be calculated for a given arclength of the cavity. In some cases with shorter cavities, the limiting solutions coincide with the formation of a stagnation point in the outer flow at both separation from the cylinder and reattachment at the end of the cavity.

(Received March 01 2006)

(Revised August 24 2006)

Keywords and phrases

  • Prandtl-Batchelor vortex;
  • trailing vortices;
  • wakes;
  • free-streamline theory;
  • integral equations.