On the development of large-sized short-scaled disturbances in boundary layers

Abstract

For high Reynolds numbers the planar nonlinear stability properties of boundary layers, as governed first by the triple-deck interaction, are discussed theoretically. When a disturbance of relatively high frequency is introduced or as the distance downstream increases in the Blasius case the characteristic length scale shortens. An account is given of the possible progress of such a disturbance, from an initially small Tollmien-Schlichting state, through a weakly nonlinear first stage that does not interrupt the amplitude growth, and thence into a fully nonlinear second stage where the Benjamin-Ono equation comes into force. Still higher frequencies point to the full Euler equations holding, although significant non-parallel flow effects then emerge. In the Euler stage, however, and in the previous second stage, bursts of vorticity from the viscous sublayer closest to the solid surface are almost certain to occur. The relations with other basic flow problems, and with turbulence-modelling, are noted, as well as the need to consider three-dimensional motion. Finally, an Appendix deals with certain issues of practical importance arising with respect to non-parallel flow effects, for example in breakaway separations or flow over surface-mounted obstacles, and points out that the slope of the local displacement in the basic flow is then a dominant controlling feature of the short-scale instabilities.