On the linear and nonlinear development of Görtler vortices

Abstract

The linear and nonlinear developments of Görtler vortices were experimentally investigated by means of hot-wire anemometer measurement. The wavelengths of the vortices were preset to be the most amplified using thin perturbation wires. Three different vortex wavelengths of 12, 15, and 20 mm were considered. These wavelengths were preserved downstream which confirm the prediction of the most amplified wavelength of Görtler vortices. The onset of the nonlinear region occurs at about the same Görtler number of 5.0 for all the wavelengths considered. In this nonlinear region, the secondary instability is initiated near the boundary layer edge, and it develops further downstream. The maximum turbulent intensity increases as the secondary instability becomes dominant in the flow. In the transition region, however, it slightly decreases before drastically increasing due to the onset of turbulence. Three maxima of intense turbulence are found in the turbulent intensity contours in the nonlinear region, which indicate the occurrence of the so-called varicose and sinuous modes of the secondary instability. Comparison with the previous available results shows that all data of maximum disturbance amplitude obtained from the same experimental setup seem to lie on a single line when they are plotted against Görtler number, regardless of the values of free-stream velocity and concave surface radius of curvature. Smaller radius of curvature results in higher vortex growth rate in the linear region due to stronger centrifugal effect. However, the vortex growth rate seems to be unaffected by free-stream velocity. The normal position of maximum disturbance amplitude reaches the maximum point exactly at the onset of nonlinear region before it drastically drops as the secondary instability is overtaking the primary instability.