On the growth of mushroomlike structures in nonlinear spatially developing Goertler vortex flow

Spatially developing longitudinal vortices, originating from upstream Goertler vortices, are studied by a finite-difference algorithm. Three-dimensional parabolized Navier–Stokes equations for a ‘‘slightly’’ concave wall and a thin boundary layer are used, in conjunction with the total (mean plus perturbation) flow quantities as dependent variables. The behavior of Goertler vortex development from the linear region to the fully nonlinear region was obtained just prior to the development of secondary instabilities and turbulence. Comparisons with the experiments are discussed, showing the development of mushroomlike features in the streamwise velocity component.