The inner viscous solution for the core of a leading-edge vortex

Abstract

In an earlier paper Hall (1961) proposed a simplified model for the vortex core formed over a slender delta wing at incidence by the rolling-up of the shear layer that separates from a leading edge. This model enabled an outer inviscid solution and an inner viscous solution for the core to be obtained from the equations of motion. However the procedure used for the inner solution led to a number of defects: in particular, the matching of the inner and outer solutions seemed unsatisfactory. In the present paper the defects are avoided by using a different procedure. The first approximation, in the sense of boundary-layer theory, is sought. A solution, in special variables, is obtained which is in the form of an asymptotic expansion containing inverse powers of the logarithm of a Reynolds number. The leading terms of the expansion are computed, and the results confirm that the inner and outer solutions are properly matched.