A RAPID-PRESSURE COVARIANCE REPRESENTATION CONSISTENT WITH THE TAYLOR-PROUDMAN THEOREM MATERIALLY FRAME INDIFFERENT IN THE 2-DIMENSIONAL LIMIT

A nonlinear variable-coefficient representation for the rapid-pressure covariance appearing in the Reynolds stress and heat-flux equations, consistent with the Taylor-Proudman theorem, is presented. The represe ntation ensures that the modelled second-order equations are frame ind ifferent with respect to rotation in a number of different flows for w hich such an invariance is required. The model coefficients are functi ons of the state of the turbulence; they are valid for all states of a mechanical turbulence, attaining their limiting values only when the limit state is achieved. This is accomplished by a special ansatz that is used to obtain - analytically - the coefficients valid away from t he realizability limit. Unlike other rapid-pressure representations in which extreme states are used to set model constants, here the coeffi cients are variable functions asymptotically consisted with-not fixed by-the limit states of the turbulence field. The mathematical principl es invoked do not specify all the coefficients in the model; undetermi ned coefficients appear as free parameters which are used to ensure th at the representation is asymptotically consistent with an experimenta lly determined equilibrium state of homogeneous sheared turbulence. Th is is done by ensuring that the modelled evolution equations have the same fixed points as those obtained from numerical and laboratory expe riments for the homogeneous shear. Results of computations of homogene ous shear, with rotation and with curvature, are shown. Results are be tter, in a wide class of planar flows for which the model has not been calibrated, than those of other nonlinear models.