Wall shear stress in Görtler vortex boundary layer flow

Abstract

The development of wall shear stress in concave surface boundary layer flows in the presence of Görtler vortices was experimentally studied by means of hot-wire measurements. The wavelengths of the vortices were preset by thin vertical perturbation wires so to produce the most amplified wavelengths. Three different vortex wavelengths of 12, 15, and 20 mm were considered, and near-wall velocity measurements were carried out to obtain the “linear” layers of velocity profiles in the boundary layers. The wall shear stress coefficient Cf was estimated from the velocity gradient of the “linear” layer. The streamwise developments of boundary layer displacement and momentum thickness at both upwash and downwash initially follow the Blasius (laminar boundary layer) curve up to a certain streamwise location. Further downstream, they depart from the Blasius curve such that they increase at upwash and decrease at downwash before finally converge to the same value due to the increased mixing as a consequence of transition to turbulence. The spanwise-averaged wall shear stress coefficient C¯f, which initially follows the Blasius curve, increases well above the local turbulent boundary layer value further downstream due to the nonlinear effect of Görtler instability and the secondary instability modes. Three different regions are identified based on the streamwise development of C¯f, namely linear, nonlinear, and transition to turbulence regions. The onset of nonlinear region is defined as the streamwise location where the C¯f begins to depart from the Blasius curve. In the nonlinear region, the spanwise distribution of Cf at the downwash becomes narrower, and there is no inflection point found further downstream.