Three-Dimensional Navier-Stokes Computations of Spatially Developing Görtler Vortices

Abstract

The Gortler flow is studied through three-dimensional incompressible Navier-Stokes computations, that solve for the spatially developing flow. By the use of inflow-outflow boundary conditions (as opposed to the temporal approach) we allow in a natural way for the development of the boundary layer, we preserve the convective nature of the Gortler instability and we do not impose a priori streamwise wavelengths (such as the wavelength of the secondary instability). Furthermore, we consider more than one vortex pair in the cross-section so that vortex interaction mechanisms are not overlooked. This is likely to be an important requirement in the selection of the secondary instability mode. The results computed in the primary instability regime are in very good agreement with experiments. To trigger the secondary instability we introduce the equivalent of a “vibrating ribbon”. The secondary instability starts as a sinuous motion of the low speed streaks. The spanwise movement of the streaks is a feature that the Gortler flow shares with shear layer structures in near-wall turbulence.