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A generalization of a class of differential length-scale equations typically used in second-order turbulence models for oceanic flows is suggested. Commonly used models, like the κ-e model and the Mellor-Yamada model, can be recovered as special cases of this generic model, and thus can be rationally compared. In addition, a method is proposed that yields a generalized framework for the calibration of the most frequently used class of differential length-scale equations. The generic model, calibrated with this method, exhibits a greater range of applicability than any of the traditional models. Stratified flows, plane mixing layers, and turbulence introduced by breaking surface waves are considered besides some classical test cases.
Umlauf et al. (Sat,) studied this question.