A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station Papa and long‐term upper ocean study site

Abstract

A simple eddy kinetic energy parameterization of the oceanic vertical mixing is presented. The parameterization scheme is based on recent works on atmospheric turbulence modeling. It is designed to simulate vertical mixing at all depths, from the upper boundary layer down to the abyss. This scheme includes a single prognostic equation for the turbulent kinetic energy. The computation of the turbulent length scales is diagnostic, rather than prognostic. In weakly turbulent regions the simulated vertical diffusivity is inversely proportional to the Brunt-Vai'sala frequency. In the first validation experiments presented here, the vertical mixing scheme is embedded into a simple one-dimensional model and used for upper ocean simulations at two very different test sites: the station Papa in the Gulf of Alaska and the Long-Term Upper Ocean Study (LOTUS) mooring in the Sargasso Sea. At station Papa the model successfully simulates the seasonal evolution of the upper ocean temperature field. At LOTUS the focus is on a short 2-week period. A detailed analysis of the oceanic heat budget during that period reveals a large bias in the bulk-derived surface heat fluxes. After correction of the fluxes the model does well in simulating the evolution of the temperature and wind-driven current. In particular, the large observed diurnal cycles of the sea surface temperature are well reproduced. During the second (windy) week of the selected period the model accounts for about two thirds of the kinetic energy of the observed upper ocean currents at periods larger than 6 hours. The local wind forcing thus appears to be the dominant generation mechanism for the near-inertial motions, which are the most energetic. The velocity simulation is especially good at the low frequencies. During the second simulated week the model accounts for as much as 78% of the kinetic energy at subinertial frequencies. The simulated mean velocity profile is reminiscent of an Ekman spiral, in agreement with the observations. 1. 16,179 16,180 GASPAR ET AL.' A SIMPLE EDDY KINETIC ENERGY MODEL FOR VERTICAL MIXING nearly optimal assimilation techniques can be associated with their discretized form [Mort et al., 1988]. Such models thus meet our basic requirements. However, they have a main weak point in the determination of a turbulent master length scale [Mellor and Yamada, 1982]. The master length can be either specified as a function of different characteristic turbulent scales or computed from a prognostic equation. In most oceanic applications [e.g., Mellor and Durbin, 1975; Klein and Coantic, 1981; Martin, 1985; AndrO and Lacar-r&re, 1985], that length is specified and specially tailored for ML modeling. It is generally dependent on the Blackadar [1962] length scale which is meaningless when several isolated turbulent regions are present in the water column. This again limits the use of such schemes in boundary layer modeling as is the case for the bulk models. On the contrary, the prognostic equation for the master length [Mellor and Yamada, 1974] is gene...

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