Effects of streamwise wall curvature variation on the nonlinear evolution of different Görtler vortices wavelengths

Abstract

In this paper, a high-order, pseudo-spectral numerical code (HOPe) is used to investigate the influence of curvature variations on the nonlinear evolution of different Gortler vortices wavelengths. The mechanism by which Gortler instability selects the wavelength of the vortex when considering boundary layer over variable curvature surface is not clearly understood. In order to investigate the influence of the wall curvature and the effects of the spanwise wavelength on the laminar–turbulent transition process, three spanwise wavelengths and four different streamwise wall curvature distributions were analyzed: constant, concave–convex, concave-flat, and periodic curvature wall. The results show concave–convex wall distribution is the most stable case. With the change from concave to convex curvature, the centrifugal effects were turned off and this tends to eliminate the inflection points from the spanwise and normal profiles of the streamwise velocity. Thus, there is evidence that the convex curvature can be useful for laminar flow control. Furthermore, the numerical results indicate that the spanwise wavelength of stationary disturbance has a significant effect on the instability phenomenon, where the largest spanwise wavelength is the most unstable case when the curvature distribution is changed.