Turbulent flow MTES

MVF methods fail in any flow where the nature of the turbulence is altered by some parametric effect, such as rotation, which does not appear parametrically in the equations of mean motion. Such effects can be included in MVF methods only by alteration of the I or rr specification, and hence MTE or MRS methods are clearly to be preferred for such cases. 

There is a more fundamental objection to the MTES idea. Recently Lumley (L3) has ai ed that the homogeneous flows upon which Eqs. (32) and (33) are based do not really reach equilibrium, and that instead the turbulence time (and length) scales continually increase. Champagne et al. (C4) experiments confirm this expectation. Hence, a structural model cannot be fully correct in homogeneous flows. 

Mellor and Herring also examine MRS closures, and show how the MTEN closure results from the MRS equations with the additional assumption of small departures from isotropy. While this approach is academically interesting, even the most weakly strained flows are far from isotropic (C4), and hence the main selling point for MTE methods is that they work very well for predicting a wide class of turbulent shear flows. Examples are given in the following section. 

The MTES approach has been advocated by Bradshaw and his coworkers (B2, B3). Their predictions for the Stanford conference must be judged among the very best. The ability of Bradshaw s MTES method to predict severe flows was demonstrated by their results for the Tillmann ledge flow, a boundary-layer flow immediately downstream of a turbulent reattachment point (judged the most difficult conference flow). Figure 15 shows their predictions at a point downstream in this flow, including results for two drastically different initial shear stress distributions. We note that the predictions are very insensitive to the initial (upstream) shear stress distribution. In spite of the modest disparity between the measured and... 

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