Development of boundary-layer flow in the presence of forced wavelength Görtler vortices

Abstract

Hot-wire measurements in the boundary layer developing on a concave surface of 2.0 m radius of curvature in the presence of forced wavelength Görtler vortices have been conducted for a free-stream velocity of 3.0 m/s. The wavelengths of vortices were preset by vertical perturbation wires of 0.2 mm diameter located 10 mm upstream of the concave surface leading edge. The velocity contours in the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices that are similar to those found in the transitional flow field. It shows the occurrence of the second instability mode that is indicated by the formation of small horseshoe eddies generated between the two neighboring vortices traveling in the streamwise direction to form mushroom-like structures as a consequence of the nonlinear growth of the Görtler vortices. The breakdown of these structures before the boundary-layer flow becomes turbulent is also shown to qualitatively predict the start of the transition in the flow. The Görtler number where the start of the transition was predicted is found to be within the range of transitional Görtler numbers previously reported for naturally developed Görtler vortices. The average of the spanwise wavelength after being normalized by ν/uτ is comparable with the generally quoted value of 100 for turbulent boundary layers.