Wave Interaction Theory and LFC

Abstract

The complex high Reynolds number flows over modern swept wings can support at least three types of hydrodynamic instability; namely Gortler, Crossflow, and Tollmien-Schlichting instability mechanisms which can all cause transition to turbulence in many flows of practical importance. In the LFC context, it is important for us to know whether the simultaneous presence of these mechanisms can cause the premature onset of transition through their mutual interaction. However, since the mechanisms can only interact in the nonlinear regime, and transition to turbulence quickly follows the onset of nonlinearity, it is clear from the outset that the massive destabilizations of flows attributed to wave interactions cannot be explained by any nonlinear interaction theory. Nevertheless, it is important to understand whether the nonlinear interactions which occur when an instability mechanism has produced a disturbance of finite size can lead to the catastrophic growth of other instabilities which would otherwise have remained small. Given that our present tools for transition prediction are so crude that they have no input from nonlinear theories, the work we discuss here is perhaps most relevant to a situation where the aim is to control a particular type of disturbance once nonlinear effects have been induced.