On the spectral distribution of the modes in nonlinear Görtler instability

Abstract

Abstract Longitudinal vortices generated by Gortler instability in a concave wall boundary layer are studied experimentally. The vortices were triggered by a wire grid upstream of the test-section leading edge. The vortices are visualized and their velocity field is measured in four axial positions. The measurements show weakly nonlinear growth and also nonlinear saturation of perturbations. Wall-normal and spanwise gradients of the velocity field calculated from the velocity measurements show that the spanwise gradients grow faster than the wall-normal gradients. It is thus inferred that the sinuous mode associated with the spanwise gradient will be the dominant instability mode. Spectral analysis of the spanwise profiles of the streamwise velocity show that seven modes suffice to represent the velocity field in the nonlinear regime. However, the amplitudes of the modes present in the velocity profiles vary with distance from the wall as with distance from the leading edge.