Boundary-layer growth

Abstract

The work presented here is an extension of that of Blasius (1908) on boundary-layer growth at a cylinder started from rest. It is shown that if an infinite plane moves in its own plane in a viscous fluid, the velocity distributions are similar at different times if the velocity V{t) of the plane is of the form V(t) = Atα or V(t) = A ect, where t is the time. These cases are then applied to the theory of boundary-layer growth and the second approximation to the velocity in the boundary layer is calculated. From this we find a first approximation for the distance travelled by the cylinder before separation starts. The second approximation to the separation distance was calculated by Blasius for α = 1, by Goldstein & Rosenhead (1936) for α = 0, and is found here for the case V(t) — A ect. Another approximate method for finding the separation distance, when separation starts at the rear stagnation point, is developed and applied to the impulsive start. The method is based on the momentum equation and assumes that the velocity profile near the rear stagnation point will always be similar to an initial profile. The numerical results are presented in the tables, and include the variation with a of the separation distance (according to the first approximation). It is hoped to use the method of Gortler (1944) to evaluate the drag on a circular cylinder and thus to discuss the initial motion of such a cylinder.