Second-Order Boundary-Layer Effects for Large Injection or Suction

Summary

The solutions of the Navier-Stokes-equations for the two dimensional incompressible flow past bodies with permeable walls are considered for small values of ε = 1/√Re and for normal velocities at the wall of the order e where 0 < α < 1. The investigation is an extension of Van Dyke’s work, [1], to intensive blowing or suction as well as an extension of the “hard-blowing” solution of classical boundary layer theory (Cole, Aroesty, [2]) to higher order effects. By using matched asymptotic expansions the solutions are found to consist of three layers: the outer flow, the layer close to the wall with non-zero vorticity but without viscosity and a free shear layer in between. The second order effects of curvature and displacement on the wall shear stress are determined. As an example the flow past a circular cylinder with normal velocities proportional cos x (x = polar angle) is considered.