Production of longitudinal vortices in the boundary layer along a concave wall

Abstract

Velocity measurements in the boundary layer along a concave wall reveal a spanwise variation having a definite wave number whether the boundary layer is laminar or turbulent. The variation is interpreted as produced by a system of vortices with axis in the streamwise direction. For the laminar boundary layer the vortices are identified with those predicted by the theory of laminar instability. The wave amplitude distribution and wave amplification rate are in good agreement with the theoretical prediction. For the turbulent boundary layer the concept of eddy viscosity is introduced to account for the observed phenomena by the theory of laminar instability. In both cases, however, the mechanism by which the wave number is determined remains an open question. Since the centrifugal force in the concavely curved boundary layer is analogous to the buoyant force in the thermally stratified boundary layer in giving rise to instability, some analogous phenomena may be expected in the boundary layer along a heated horizontal wall.