Spanwise velocity component in nonlinear region of Görtler vortices

Abstract

The spanwise velocity component of Görtler vortices in a concave surface boundary layer flow was experimentally studied by means of hot-wire anemometer measurements. For this purpose, the wavelength of the Görtler vortices was pre-set to the most amplified wavelength of 12 mm at free-stream velocity of 2.8 m/s, by a series of thin perturbation wires placed near to the concave surface leading edge. The streamwise and spanwise velocity components, respectively, u and w, in the nonlinear region of Görtler vortices were measured using an X-wire probe. The secondary motion induced by the free-stream disturbances in the vortex's head region is observed to be amplified by the appearance of secondary instability. The ∂w/∂y iso-shear contours form alternate positive and negative shear layers across the boundary layer in the upwash region. On the other hand, two pairs of anti-symmetric structures are observed in the ∂w/∂z iso-shear contours near the wall and vortex's head. The $\overline {w^{\prime 2 }}$w′2¯ contours have two intense regions at the stem and head of the vortex structures. The most unstable characteristic frequency of secondary instability is found exactly at the maxima of the contours. The Reynolds shear stress $-\overline {u^{\prime} w ^{\prime}}$−u′w′¯ contour is anti-symmetric in z-direction about the upwash with a pair of two intense regions of positive and negative shears at both the stem and head of the vortices. The $ - \overline {u^{\prime} w^{\prime} } \partial u/\partial z$−u′w′¯∂u/∂z contours reveal that the energy conversion mechanism occurs intensely on the sides of the vortex's stem.