An investigation of the importance of third-order correlations and choice of length scale in mixed layer modelling

A study of the mixed-layer deepening is conducted with a one-dimensional, third-order closure turbulence model. An approximate model that retains second-order terms in ratios of characteristic turbulence to mean-field scales is also developed. Development of the mixed layer is initiated by applying a constant wind stress and heat flux to an ocean of linear initial stratification. Results show that inside the mixed layer, the contribution of the triple-correlation terms to the turbulent energy equation is negligible. In the entrainment zone, the triple-correlation terms are of the same order of magnitude as the other significant terms. The net effect of the triple-correlation terms is to deepen the mixed layer. Various length scale prescriptions have been considered and compared against each other. The entrainment rates are calculated for a chosen range of parameter space and compared against the experimental results of Kato and Phillips (1969).