Cavity Flow in a Boundary Layer

A numerical-and-analytical method for solving cavity flows in a vortex incidence flow is proposed. The continuous vorticity arbitrary displayed in the flow field is replaced by discrete vortex lines coinciding with stream lines. The flow between these lines is assumed to be vortex free. The problems of the flow in channels formed by stream/vortex lines and the problem of the cavity flow in a jet of a finite width connected to each other by the derived interaction conditions are solved by using complex variable theory. The numerical procedure is based on the method of successive approximations and adopted to investigate the effect of the velocity gradient in a boundary layer on parameters of the cavity flow. The presented calculations show that, at some fixed cavity length, the cavity number and drag coefficient decreases with the increase of the boundary layer width.