RECEPTIVITY MECHANISMS FOR GORTLER VORTEX MODES

The receptivity problem for Gortler vortices induced by wall roughness or freestream disturbances is reviewed. To date, receptivity studies for this problem have been exclusively linear in character and here we show how the roughness and freestream disturbance mechanisms can each play dominant or inconsequential roles as possible routes to transition. The importance of each process is dependent on the exact situation at hand. For example, distributed wall-roughness elements tend to be more important in the generation of O(1) wave-number vortices than are isolated roughness patches whilst variations in the freestream velocity can easily provoke high wave-number disturbances on which roughness distributions typically have negligible effect. It has only been in recent times that the influence a spanwise component of the underlying basic boundary-layer flow may have on the Gortler mechanism has come to be appreciated. ln some new computations we show that the imposition of such a spanwise component can lead to an increase in the coupling coefficient (a measure of the efficiency of a generating process) for modes provoked by wall roughness. However, such crossflow tends to reduce the global amplification rate of the most unstable mode so has the overall effect of restricting vortex growth downstream of any roughness element. We also demonstrate how the nonparallelism of Gortler vortices implies that conclusions concerning vortex receptivity properties can only be drawn after taking full account of upstream conditions and the precise form of the generating mechanism but it appears that for a large class of flows distributed wall forcing is more important in the provocation of modes than are either isolated roughness or freestream disturbances.