Brian Crenna

Thesis Approved May 1994

Re-evaluating the Mellor-Yamada Turbulence Closure Hierarchy: Analytical and Numerical Studies

The Mellor-Yamada turbulence closure scheme is among the most popular simple turbulence parameterizations for use in numerical geophysical fluid simulations. Currently, its applications range from one-dimensional atmospheric to three-dimensional oceanic models. Although typically implemented in a form described more than a decade ago by its authors, recent studies reveal that it should be updated. In comparisons with results from both theoretical analyses and large eddy simulation (LES) model tests, several approximations used in the model have been found to be inadequate; these studies have suggested alternatives which, if incorporated, should produce a more realistic model. Certain constants required by the model, originally determined using data from laboratory flows, were found to be in need of adjustment for use in the atmospheric boundary layer.

In this study, the Mellor-Yamada closure hierarchy is re-evaluated in light of the mentioned numerical and theoretical work. Sensitivity of the model to changes in its empirical constants is investigated. Even for modest and justifiable changes, resulting differences in model behavior are seen to be dramatic; it is evident that their reliance on the empirical constants, while perhaps unavoidable, represents a significant limitation of the MY closure schemes. Two new constraints on the choice of these constants are described. A set of constants published for use with the MY model is seen to violate these constraints, and the model consequently exhibits unrealistic properties when applied to stable stratification. The effects of replacing many of the original closure assumptions by more accurate terms are examined; changes requiring only slight adjustments to the form of the original model are emphasized. The behaviour of models which result from the recommended substitutions can, nonetheless, be quite different from that of the original. To specify the constants associated with the modified schemes will require comparisons with empirical and numerical modeling data to an extent not possible in the present study.

Brian can be reached at