ON SPATIAL EVOLUTION OF LONG-WAVELENGTH GÖRTLER VORTICES GOVERNED BY A VISCOUS-INVISCID INTERACTION PART 1: THE LINEAR CASE

Abstract

Abstract : The generation of long-wavelength, viscous-inviscid interactive Gortler vortices is studied in the linear regime by numerically solving the time-dependent governing equations. It is found that time dependent surface deformations, which assume a fixed nonzero shape at large times, generate steady Gortler vortices that amplify in the downstream direction. Thus, the Gortler instability in this regime is shown to be convective in nature, contrary to the earlier findings of Ruban and Savenkov. The disturbance pattern created by steady and streamwise-elongated surface obstacles on a concave surface is examined in detail, and also contrasted with the flow pattern due to roughness elements with aspect ratio of order unity on flat surfaces. Finally, tile applicability of the Briggs-Bers criterion to unstable physical systems of this type is questioned by providing a counterexample in the form of the inviscid limit of interactive Gortler vortices.