The linear growth of Görtler vortices

Abstract

Abstract Measurements are presented of the streamwise velocity variation within a laminar boundary layer on a concave surface of 4-m radius of curvature for free-stream velocities of 7.5 and 10 m/s. The measured variation was consistent with the presence of counter-rotating vortices resulting from the Gortler instability. Contour plots of velocity and turbulence intensity show that the vortices occur in discrete pairs centred about upwash locations, rather than in a continuous row of counter-rotating vortices modelled by the stability analysis. Comparison with the normal-mode linear stability analysis indicates that the experimental data lie in a region of the stability chart for which the two observed conditions of streamwise development at constant wavelength and constant growth rate coincide. Disturbance velocity profiles compare favourably at streamwise positions for which the linear stability analysis is appropriate. Detailed comparison with the linear stability analysis indicates that the measured growth rates are considerably lower than those obtained from theory. (This is attributed to the limitations of the normal-mode analysis as well as to the fact that the observed vortices occur in discrete pairs often separated by regions of relatively undisturbed flow.) Although measured growth rates obtained by considering individual vortices were found to be greater than those obtained using spanwise-averaged velocity profiles.