An investigation of recirculating flow in a driven cavity

The problem of steady incompressible laminar shear-driven flow in a two-dimensional quarter-circular cavity is discussed. An analytical solution is presented to the continuity and momentum equations at leading order for the case when the Reynolds number (Re) is much smaller than one. In addition, the O(Re) correction is computed numerically, and comparison of the two-term expansion for the streamfunction with a full numerical computation of the Navier-Stokes equations yields good agreement for a nominal value of Re as large as 100. Solutions for Re≫1 are also presented; these indicate several extra features that are not present in the classical driven-cavity problem, pertaining in particular to the flow direction and to the manner in which the governing equations should be correctly scaled.