On the determination of the closure parameters in higher-order closure models

Abstract

In higher-order closure models at least the pressure redistribution and the dissipation of the turbulent kinetic energy and the temperature variance have to be parameterized. Due to this, the introduction of proportionality coefficients — the so-called closure parameters — is forced, which have to be determined before the model is used. We compare a group of models which use the return-to-isotropy hypothesis (Rotta, 1951) to describe the pressure redistribution and assume local isotropy for the smallest eddies in order to parameterize the dissipation. Special concern is given to the method of Mellor and Yamada (1982). Some of the closure parameters are re-derived on the basis of sensitivity studies requiring that both shear production and buoyancy behave in a realistic way if pressure redistribution or dissipation is changed by varying the closure parameters. This set of parameters is compared with those obtained by fitting to experimental data, by use of the Monin-Obukhov similarity theory and by considering ratios of variances, covariances and mean flow gradients, respectively. It is shown that the various sets of closure parameters are at least of the same order. The differences give some insight into the advantages and disadvantages of the various determination procedures. However, the general accordance of the different parameter sets supports the assumption of universal constants.