Turbulent Wall-Layer Vortices

Turbulent flow near walls is common in a wide variety of engineering applications, including a spectrum of external flows encountered on aircraft and ship surfaces and the blades of gas turbines. In many situations, the external flow field is effectively irrotational and laminar. However, once the Reynolds number exceeds a certain threshold level, a process of amplification of small disturbances in the flow field causes the boundary layer near the surface to undergo transition to a fully turbulent state; here the Reynolds number is defined by Re = U _o L/v, where U _o is the basic flow speed, L is a length characteristic of the body and v is the kinematic viscosity. There are at least three distinct routes to boundary-layer turbulence. In well-controlled experiments, it is possible to delay the onset of transition to fairly high Reynolds number. However, at some stage, small disturbances in the boundary layer start to grow and the onset of transition is heralded by the appearance of Tollmein-Schlichting (TS) waves (Tani 1969; Reshotko 1976, 1988). In a process which is not entirely understood, the TS waves break down as they advect downstream in an apparently nonlinear process that culminates in the formation of vortices. These vortices have a characteristic shape reminiscent of a woman’s hairpin common in the 1950’s and classically have been referred to as hairpin vortices; it should be emphasized, however, that modern usage of this terminology does not necessarily imply a completely symmetric vortex structure. Once this type of vortex appears, a process of regeneration and production of more vortices ensues; the flow field becomes progressively more complex such that the end-stages of transition, as well as the fully turbulent boundary layer further downstream, are characterized by a rich and complex tangle of vortices.