Behaviour of a vortex sheet separating from a smooth surface

The behavior of a vortex sheet embedded in an irrotational steady flow and springing from a separation line on a smooth body is studied around the separation line. It is shown that the vortex sheet is tangential to the wall along the separation line. Assuming that the body is slender and the separation line is highly swept, it is shown that the exponent which defines how rapidly the sheet departs from the body must take one of a set of discrete values. The smallest of these, corresponding to the most rapid departure of the sheet, implies an infinitely large adverse pressure gradient on the upstream side of the separation line. The next largest exponent avoids this. The implications for modeling separated flows are discussed.