Centrifugal instabilities in curved compressible wakes

This investigation is concerned with the linear development of Gortler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a curved mixing-layer system. The Gortler modes were previously found to exist within curved compressible mixing layers by Owen et al. [Phys. Fluids 8, 2506 (1997)]. This study extends that investigation and demonstrates the effect a wake has on the growth rate and location of such modes. The investigations were made by examining the growth rate and the location of the Gortler modes in the limit of large Gortler number and high wave number within the wake-dominated curved compressible mixing-layer systems based on three wake flow models. An analytic Gaussian wake profile is first used to model the behavior of the basic flow within the mixing layer at the trailing edge of the splitter plate. It is found that the wake has an amplification effect on the growth of the Gortler instability within the concavely curved or "unstably" curved compressible mixing layers. It is also found that within the convexly curved or "stably" curved compressible mixing layers wake modes can occur that behave differently to the "thermal modes," which were previously found within the plain curved compressible system by Owen et al. Another analytic composite model which has some practical applications is then used to predict the behavior of the modes within the systems. Solutions from a numerical wake flow model have been compared with the predictions based on the analytic wake flow models. (C) 2009 American Institute of Physics. [doi:10.1063/1.3241990]