A generic length-scale equation for geophysical turbulence models

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 k-epsilon 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.