If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization

Abyssal recipes II: energetics of tidal and wind mixing

▪ AbstractThe coexistence in the deep ocean of a finite, stable stratification, a strong meridional overturning circulation, and mesoscale eddies raises complex questions concerning the circulation energetics. In particular, small-scale mixing processes are necessary to resupply the potential energy removed in the interior by the overturning and eddy-generating process. A number of lines of evidence, none complete, suggest that the oceanic general circulation, far from being a heat engine, is almost wholly governed by the forcing of the wind field and secondarily by deep water tides. In detail however, the budget of mechanical energy input into the ocean is poorly constrained. The now inescapable conclusion that over most of the ocean significant “vertical” mixing is confined to topographically complex boundary areas implies a potentially radically different interior circulation than is possible with uniform mixing. Whether ocean circulation models, either simple box or full numerical ones, neither explic...

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Vertical mixing, energy, and the general circulation of the oceans

Ocean microstructure data show that turbulent mixing in the deep Brazil Basin of the South Atlantic Ocean is weak at all depths above smooth abyssal plains and the South American Continental Rise. The diapycnal diffusivity there was estimated to be less than or approximately equal to 0.1 x 10(-4) meters squared per second. In contrast, mixing rates are large throughout the water column above the rough Mid-Atlantic Ridge, and the diffusivity deduced for the bottom-most 150 meters exceeds 5 x 10(-4) meters squared per second. Such patterns in vertical mixing imply that abyssal circulations have complex spatial structures that are linked to the underlying bathymetry.

https://science.sciencemag.org/content/sci/276/5309/93.full.pdf

Spatial variability of turbulent mixing in the Abyssal Ocean

Résumé The ocean engine of NEMO (Nucleus for European Modelling of the Ocean) is a primitive equation model adapted to regional and global ocean circulation problems. It is intended to be a flexible tool for studying the ocean and its interactions with the others components of the earth climate system over a wide range of space and time scales. Prognostic variables are the three-dimensional velocity field, a linear or non-linear sea surface height, the temperature and the salinity. In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction, a full or partial step z-coordinate, or s-coordinate, or a mixture of the two. The distribution of variables is a three-dimensional Arakawa C-type grid. Various physical choices are available to describe ocean physics, including TKE, GLS and KPP vertical physics. Within NEMO, the ocean is interfaced with a sea-ice model (LIM v2 and v3), passive tracer and biogeochemical models (TOP) and, via the OASIS coupler, with several atmospheric general circulation models. It also support two-way grid embedding via the AGRIF software. Le moteur océanique de NEMO (Nucleus for European Modelling of the Ocean) est un modèle aux équations primitives de la circulation océanique régionale et globale. Il se veut un outil flexible pour étudier sur un vaste spectre spatiotemporel l’océan et ses interactions avec les autres composantes du système climatique terrestre. Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer linéaire ou non, la temperature et la salinité. La distribution des variables se fait sur une grille C d’Arakawa tridimensionnelle utilisant une coordonnée verticale z à niveaux entiers ou partiels, ou une coordonnée s, ou encore une combinaison des deux. Différents choix sont proposés pour décrire la physique océanique, incluant notamment des physiques verticales TKE, GLS et KPP. A travers l’infrastructure NEMO, l’océan est interfacé avec des modèles de glace de mer, de biogéochimie et de traceurs passifs, et, via le coupleur OASIS, à plusieurs modèles de circulation générale atmosphérique. Il supporte également l’emboı̂tement interactif de maillages via le logiciel AGRIF.

NEMO ocean engine

Scaling of the turbulent energy equation suggests the balance of terms in the ocean is between turbulent production, dissipation and the loss to buoyancy. In this paper two models for the source of oceanic turbulence are considered; namely, production by the Reynolds stress working against a time variable mean shear, and the gravitational collapse of Kelvin-Helmholtz instabilities. Both of these shear instabilities are believed to be important in the ocean. Using values for the critical flux Richardson number and the measurements from studies of Kelvin-Helmholtz instabilities, the efficiency of turbulent mixing is shown to be comparable for the two models. Therefore, a general relationship between the dissipation rate and the buoyancy flux due to the small-scale turbulent velocity fluctuations is derived. The result is expressed as an upper bound on the value of the turbulent eddy coefficient for mass Kρ ⩽ 0.2ϵ/N2. Values of Kρ are calculated from recent oceanic measurements of energy dissipation...

Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements

Measurements by free fall instruments, in the San Diego Trough, the Florida Current, and the central Pacific, reveal the detailed structure of the vertical component of the oceanic temperature gradient. The temperature changes are concentrated into regions on the order of a meter thick wherein the measured gradients are often more than ten times the average gradient. The horizontal extent of the regions of high gradient is greater than 750 meters in the seasonal thermocline off San Diego, but is only a few hundred meters at depths greater than 400 meters. Fine scale measurements show that the layers of high gradient consist of even finer fluctuations in gradient which are only a few centimeters thick. Time scales of the thinnest of these regions of high gradient are of the order of five minutes. The data also yields an estimate of the entropy generation. According to the results of an idealized model relating entropy generation to the turbulent heat transport, only 240 to 700 ergs per cm.2 per se...

Oceanic fine structure

A free-fall oceanographic instrument capable of producing direct estimates of the local rate of energy dissipation has been developed. The velocity sensor in an adaptation of the two-component airfoil probe to the oceanic environment. Spectra of the velocity data show that the instrument achieves complete spatial resolution of the vertical current shear and there is no apparent contamination of the signal from vibrations or body motions in the frequency range contributing to the variance of the shear. The energy dissipation is proportional to the variance of the vertical shear. Thus, it is possible to estimate the energy dissipation without comparing the velocity spectra to any “universal curve.”

Vertical Profiling of Velocity Microstructure

The spectral response of thermistors

The residual circulation in the western Labrador Sea is discussed in the light of recent current data combining information from moored instruments, satellite-tracked surface buoys, and geostrophic calculations. The characteristic features of the surface flow pattern observed near the mouth of Hudson Strait are explained qualitatively in terms of the response of the flow to the form of the coastline and to the nearshore bathymetry.

Thomas R. Osborn

Papers

Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements

Oceanic fine structure

Vertical Profiling of Velocity Microstructure

The spectral response of thermistors

Surface circulation in the Western Labrador Sea