Secondary Instability of Boundary Layers

Abstract

The problem of transition from laminar to turbulent flow in viscous bound­ ary layers is of great practical interest. The low skin-friction coefficient of laminar boundary-layer flow is very attractive to those who lay out the engines or pay the fuel for high-speed vehicles such as airplanes. However, the low mixing of fluid properties such as chemical species, heat, or momen­ tum may be intolerable for others who design these engines or cope with the danger of separation in adverse pressure gradients; they may clearly prefer a turbulent state of the flow. Therefore, it would be highly desirable to at least predict, if not to control, whether the flow under consideration is laminar or turbulent. The tremendous efforts of decades of intense research, however, have been to little avail (Reshotko 1976). The empirical en-criterion is still the standard tool in engineering practice, although it is known to ignore essential ingredients of the physics of transition and therefore may dangerously mislead if used beyond the supporting data base. Numerical transition simulations have gained reliability in repro­ ducing the transition process in sufficient detail to extract information unobtainable from laboratory experiments. However, the inherent assumptions of stream wise periodicity and temporal growth of the bound­ ary layer, in addition to the uncertainty of initial conditions, prevent predicting transition in practice. Hence, theory still holds an important place in identifying inherent mechanisms and structures of the transition process and in explaining otherwise unintelligible observations. The past decade saw some important progress in stability theory, slow or fast, depending on the reader's judgment ..