In the stably stratified interior of the ocean, mesoscale eddies transport materials by quasiadiabatic isopycnal stirring. Resolving or parameterizing these effects is important for modeling the oceanic general circulation and climate. Near the bottom and near the surface, however, microscale boundary-layer turbulence overcomes the adiabatic, isopycnal constraints for the mesoscale transport. In this paper we present a formalism for representing this transition from adiabatic, isopycnally-oriented mesoscale fluxes in the interior to the diabatic, along-boundary mesoscale fluxes near the boundaries. We propose a simple parameterization form and illustrate its consequences in an idealized flow. We emphasize that the transition is not confined to the turbulent boundary layers, but extends into the partially diabatic transition layers on their interiorward edge. A transition layer occurs because of the mesoscale variability in the boundary layer and the associated mesoscale-microscale dynamical coupling.
We propose new dynamical equations to describe fully developed turbulence. We begin with the Wyld equations ͑WE͒, which are exact solutions of the NSE. The WE, and their Langevin-like representation, show that nonlinearities induce a turbulent force f t ͑k͒ and a turbulent viscosity t (k), which are given by an infinite series of Wyld diagrams. The series for t (k) is renormalizable, and its sum can be found using RNG methods. The result, Eq. ͑2a͒, holds for stirring forces f ext with an arbitrary correlation function and generalizes previous RNG results, which neglected f t and were limited to power law ϳk 1Ϫ2⑀ . To recover Kolmogorov law, these earlier RNG-based theories were forced to introduce an ad hoc stirring force with a prescribed ϳk Ϫ3 . By contrast, we show that ϳk Ϫ3 belongs to , which is the correlation function of f t , and that in the inertial range f t ӷ f ext . The series for cannot be summed because of a nonrenormalizable infrared divergence ͑IR͒ with an infinite number of divergent irreducible diagrams. To overcome this difficulty, we use the well-accepted notion of local energy transfer and we derive an expression for the energy flux ⌸(k), Eq. ͑2d͒, as well as a dynamical equation for the energy spectrum E(k), Eq. ͑2b͒. We also construct the dynamical equations for Reynolds stress spectra ͑solved in papers II and III͒. An analogous approach is developed for the temperature field. The model contains no free parameters. Some of its predictions are Kolmogorov spectrum E(k)ϳk Ϫ5/3 with Koϭ 5 3 , in agreement with recent data; temperature spectrum in the inertial-convective region E ϳBa ⑀ Ϫ1/3 ⑀ k Ϫ5/3 , in agreement with the data; Batchelor constant Baϭ t Ko. In addition, in papers II and III we carry out extensive comparisons with the laboratory, DNS, LES data, and phenomenological models. The model can be used to construct a subgrid model for LES calculations.
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