On The Secondary Instability Of The Most Dangerous Goertler Vortex PDF Download

Recent theoretical work has shown that strongly nonlinear, high wavenumber Gortler vortices developing within a boundary layer flow are susceptible to a secondary instability which takes the form of travelling waves confined to a thin region centered at the outer edge of the vortex. This work considered the case in which the secondary mode could be satisfactorily described by a linear stability theory and in the current paper our objective is to extend this investigation into the nonlinear regime. At this stage not only does the secondary mode become nonlinear but it also interacts with itself so as to modify the governing equations for the primary Gortler vortex. In this case then, the vortex and the travelling wave drive each other and, indeed, the whole flow structure is described by an infinite set of coupled, nonlinear differential equations. A Stuart-Watson type of weakly nonlinear analysis of these equations is undertaken and it concludes in particular, that on this basis there exist stable flow configurations in which the travelling mode is of finite amplitude. Impactions of our findings for practical situations are discussed and it is shown that the theoretical conclusions drawn here are in good qualitative agreement with available experimental observations.