On the calculation of separation bubbles

The interactive boundary-layer equations for a flat plate are solved numerically when the external velocity field is piecewise linear and would provoke separation if the response of the boundary layer were neglected. A comparable problem had already been solved by Briley using the full Navier–Stokes equations. The equations are solved for various values of the Reynolds number and x 0 , a parameter defining the corner point of the external velocity. It is found that flows with a limited region of separation can be computed, but that, if x 0 is too large, the numerical procedure breaks down. Furthermore, this maximum value is a decreasing function of R and seems to approach the value 0.12 predicted by classical theory as R → ∞. Comparison with Briley's results indicate a reasonable agreement except that different values of x 0 are appropriate. It is conjectured that, once x 0 increases above the acceptable maximum, rapid changes occur in the flow properties when R is large.