Search

Abstract The representation of turbulent fluxes during oceanic convective events is important to capture the evolution of the oceanic mixed layer. To improve the accuracy of turbulent fluxes, we examine the possibility of adding a non‐local component in their expression in addition to the usual downgradient part. To do so, we extend the k–ε algebraic second‐moment closure by relaxing the assumption on the equilibrium of the temperature variance θ′2‾. With this additional evolution equation for the temperature variance, we obtain a k–ε–θ′2‾ model (the “kεt” model) which includes a non‐local term for the temperature flux. We validate this new model against Large Eddy Simulations (LES) in three test cases: free convection (FC), wind‐driven mixing, and diurnal cycle (DC). For wind‐driven mixing, kεt is equivalent to k–ε. However, in the presence of a buoyancy flux (FC and DC), we find that the vertical profile of temperature of the LES is better captured by kεt than k–ε. Particularly, the non‐local term increases the fraction of the mixed layer that is stably stratified. For FC, this fraction is near 50% for both kεt and the LES, whereas the k–ε value is 20%. We show that this improvement is due to a better representation of the temperature variance in the inner part of the mixed layer. This better representation is mainly caused by the diffusion of temperature variance, which is described by kεt and not by k–ε.

Abstract The ocean surface mixed layer plays a crucial role as an entry or exit point for heat, salt, momentum, and nutrients from the surface to the deep ocean. In this study, we introduce a framework to assess the evolution of the mixed layer depth (MLD) for realistic forcings and preconditioning conditions. Our approach involves a physically‐based parameter space defined by three dimensionless numbers: λs representing the relative contribution of the buoyancy flux and the wind stress at the air‐sea interface, Rh the Richardson number which characterizes the stability of the water column relative to the wind shear, and f/Nh which characterizes the importance of the Earth's rotation (ratio of the Coriolis frequency f and the pycnocline stratification Nh). Four MLD evolution regimes (“restratification,” “stable,” “deepening,” and “strong deepening”) are defined based on the values of the normalized temporal evolution of the MLD. We evaluate the 3D parameter space in the context of 1D simulations and we find that considering only the two dimensions (λs, Rh) is the best choice of 2D projection of this 3D parameter space. We then demonstrate the utility of this two‐dimensional λs − Rh parameter space to compare 3D realistic ocean simulations: we discuss the impact of the horizontal resolution (1°, 1/12°, or 1/60°) and the Gent‐McWilliams parameterization on MLD evolution regimes. Finally, a proof of concept of using observational data as a truth indicates how the parameter space could be used for model calibration.