Coupled Batchelor flows in a confined cavity

Steady, inviscid, incompressible two-dimensional flow in a quarter-circular cavity containing two vortex patches is investigated. A two-parameter family of solutions, characterized by any two out of the positions of the separation and reattachment points of the main eddy, the tangential velocity at separation and the ratio of the core vorticities, is identified and computed numerically. It is found that solutions can only be obtained for a rather narrow band of combinations of these parameters; the reasons for this constraint are discussed. Finally, we consider whether any of the coupled Batchelor flow solutions actually does represent the limit of high Reynolds number flow by comparing the inviscid results with those of earlier Navier–Stokes computations (Vynnycky & Kimura 1994). Agreement for the position of the dividing streamline and the location of the centre of the main core proves to be very encouraging, and suggestions are made as to the possible future development of such a two-eddy model.