Material Spike Formation in a Turbulent Mean Flow near Separation

Since the work of Prandtl was published in 1904, boundary-layer separation in steady two-dimensional flows has been defined by the point where the wall shear-stress vanishes on the surface. One hundred years later, Haller (2004) devised a theory for the analysis of unsteady two-dimensional flows, where Prandtl’s criterion has been known to fail. In his presentation, Haller introduced the notion of a material spike, defined as the convergence and subsequent ejection of fluid particles from the vicinity of the surface. Interestingly, while the material spike offers a convincing visual description of flow separation, its origin on the wall, recently referred to as the “spiking point”, differs from Prandtl’s separation point, even in the case of steady two-dimensional flows.

In the present work, we investigate material spike formation in two-dimensional velocity fields from a separating turbulent diffuser flow. We adopt a pragmatic perspective by looking at the time-averaged velocity fields only, as has often been done with Prandtl’s criterion in the past. Hence, we are investigating the formation of a steady-in-the-mean material spike. We consider datasets obtained from both an experimental campaign using Particle Image Velocimetry and from numerical simulations using the Reynolds-Averaged Navier Stokes equations. In both cases we show that regardless of the diffuser angle, the spiking point lies very close to the diffuser corner and differs from the location of zero wall shear-stress. We discuss the consequence of this result for the classification of turbulent separated flows, and we further investigate the validity of a criterion recently proposed to determine the position of the spiking point.