Mellor-Yamada simplified second-order closure models: Analysis and application of the generalized von Karman local similarity hypothesis

Abstract

Mellor-Yamada's “superequilibrium” Level 2 and Level 1 models are analyzed using the Monin-Obukhov theory framework. Yamada's (1975) analysis is supplemented by a discussion of the realizability requirements posed on model constants and by the inclusion of the master-length scale problem. The generalized von Karman local similarity hypothesis (Laikhtman, 1979) is examined as an alternative closure hypothesis for second-order models. A systematic method of model examination is used. First, a family of models, consisting of Level 1 and Level 2 Reynolds-stress equation sets and different length-scale hypotheses (Prandtl's, generalized von Karman's), is built. Next, asymptotic characteristics of individual models are investigated and compared with similarity predictions. Monin-Obukhov universal functions for turbulent energy, space scale and temperature variance, derived from the models, are compared with experimental surface-layer data. Generally, models employing the stability-dependent generalized von Karman hypothesis perform better than those that use the conventional Prandtl mixing-length concept. The choice amongst the von Karman type models is still ambiguous. However, the Level 1 model with a stability-dependent generalized von Karman length scale seems to be the best of those considered.