EFFECT OF PRESSURE-GRADIENTS ON THE STABILITY OF 3-DIMENSIONAL BOUNDARY-LAYERS

Cross-flow is responsible for the earlier instability of three-dimensional boundary layers than that of two-dimensional ones on aeronautical wings. Its strength is governed primarily by the pressure gradients p(x) and p(y) in the directions normal and parallel to the leading edge, respectively, as well as by the sweep angle gamma of a wing. A typical boundary layer subject to those effects may be the flow on a yawed wedge placed under the pressure linearly varying along the leading edge. An exact solution to the boundary-layer equations is obtained for such a flow state, and its stability characteristics are examined by the use of the Orr-Sommerfeld equation, with particular attention to the dependence of critical Reynolds numbers on the two pressure gradients. It is found that, in the region of a favorable pressure gradient p(x) < 0, an appropriate choice of p(y) can restrain the cross-flow at a very weak level and a very stable boundary-layer flow with a high critical Reynolds number can be achieved in consequence.