Modelling transonic flows with second-moment closure

It is now generally accepted that statistical turbulence models are unlikely, ever, to enable highfidelity predictions of massively-separated flows, especially if separation occurs from curved three-dimensional surfaces. In such circumstances, even the most elaborate turbulence models are ill-equipped to capture the dynamics associated with highly-unsteady and intense large-scale motions that arise in massive separation. It is this realisation that has given substantial impetus to Large Eddy Simulation as the method of choice for predicting strongly separated flows. In contrast, turbulence models are well suited to thin shear flows and flows that contain thin, elongated recirculation zones, in which case the strain field is simpler and the large-scale dynamics significantly weaker. One class of flows in which some statistical models are found to perform well includes shock-affected boundary layers in transonic or supersonic flow, collectively referred to under the heading shock-boundary-layer interaction. Some examples are shown in Fig. 1. In the late 1990s, a substantial research effort was in progress at UMIST (University of Manchester Institute of Science and Technology) in which Batten et al (1999) and Leschziner et al (2001) developed and validated advanced turbulence models for twoand three-dimensional shock-affected flows. These efforts focused specifically on Reynolds-stress-transport models, with particular emphasis placed on a variant that incorporated a cubic pressure-strain model and terms that made the model comply with the asymptotic state of two-component turbulence at the wall.