Comparative Analysis of Four Second-Moment Turbulence Closure Models for the Oceanic Mixed Layer

Abstract

In this comparative study, four different algebraic second-moment turbulence closure models are investigated in detail. These closure schemes differ in the number of terms considered for the closure of the pressure–strain correlations. These four turbulence closures result in the eddy-diffusivity principle such that the closure assumptions are contained in dimensionless so-called stability functions. Their performance in terms of Prandtl number, Monin–Obukhov similarity theory, and length scale ratios are first tested against data for simple flows. The turbulence closure is then completed by means of a k–ϵ two-equation model, but other models such as the two-equation model by Mellor and Yamada could also be used. The concept of the steady-state Richardson number for homogeneous shear layers is exploited for calibrating the sensitivity of the four models to shear and stable stratification. Idealized simulations of mixed layer entrainment into stably stratified flow due to surface stress and due to free convection are carried out. For the latter experiment, comparison to recent large eddy simulation data is made. Finally, the well-known temperature profile data at OWS Papa are simulated for an annual cycle. The main result of this paper is that the overall performance of the new second-moment closure model by Canuto et al.—expressed as nondimensional stability functions—is superior compared to the others in terms of physical soundness, predictability, computational economy, and numerical robustness.