The instantaneous structure of mildly curved turbulent boundary layers

Abstract

Even mild longitudinal wall curvature is known to produce significant effects on the time-averaged turbulent transport in a boundary layer. The present study was undertaken to study the manner in which the instantaneous structure of turbulence in the boundary layer responds to mild streamline curvature. Both convex and concave boundary layers with a boundary-layer thickness to wall radius ratio of about 0·01 were studied. Attention was directed mainly to two events characterizing the instantaneous turbulence structure. These were the so-called ‘bursting’ and ‘zero-crossing’. Quantitative data on the statistics of these events were obtained using a combination of analog instrumentation and visual counting (from continuous film records). These data were compared with data from flat-wall boundary layers obtained from similar signal-processing techniques. The results indicate that neither the individual nor the joint statistics of these events are significantly affected by curvature in the vicinity of the wall. On the other hand, curvature seems to affect appreciably at least some properties of these events at large distances from the wall. Careful examination of these results shows, however, that neither the process of turbulent production near the wall nor the turbulent dissipative process anywhere in the boundary layer is significantly affected by mild curvature. Apparent curvature effects on the instantaneous structure in the outer part of the boundary layer can be explained as being due to the strong effect of streamline curvature on the turbulent diffusion process. This explanation is consistent with previous observations of the time-averaged structure of the flow. The results of the present study indicate the need to re-examine some of the recent turbulence models for curved flows that involve modification of the production and dissipation terms rather than the diffusion term in the transport equations.