THE NONLINEAR EVOLUTION OF CENTRIFUGAL INSTABILITIES IN CURVED, COMPRESSIBLE MIXING LAYERS

The nonlinear development of Gortler vortices in a curved compressible mixing layer is studied. It has been shown both experimentally and th eoretically that the curved mixing layer can support a centrifugal mod e, which is believed to be similar to the Gortler vortex. This study f ollows the corresponding incompressible study of Seddougui sz Otto [Pr oceedings of the IUTAM Symposium on Nonlinear Instability and Transiti on in Three-Dimensional Boundary Layers, edited by P. W. Duck and P. H all (Kluwer Academic, Amsterdam, 1995)] and attempts to demonstrate th e effect compressibility has on the growth of such modes. The formulat ion follows that of Hall & Lakin [Proc. R. Soc. London, Ser. A 415, 42 1 (1988)] for the corresponding incompressible boundary-layer problem, and utilises a stream function formulation to solve the governing equ ations. We will present the nonlinear structure of the so-called therm al modes, whose linear counterparts were first discovered in Owen. Sed dougui gr Otto [Phys. Fluids 9, 2506 (1997)]. A brief discussion will be made concerning the effect of the nonlinear modes on the inherent K elvin-Helmholtz modes of instability, which may have significant ramif ications in flows dominated by this form of instability. (C) 1998 Amer ican Institute of Physics.