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

Numerical study of mixed convection in a partially heated nanofluid-filled lid driven cavity with internal heat generation and having a partial flexible wall was performed. The bottom wall of the triangular enclosure is moving with constant speed and left vertical wall is partially heated. The inclined wall of the cavity is cooled and partially flexible. The governing equations are solved with Galerkin weighted residual finite element method. The effects of Richardson number (between 0.05 and 50), internal Rayleigh number (between 10 4 and 10 8 ), size and elastic modulus of the partial flexible wall and nanoparticle volume fraction (between 0 and 0.04) on the fluid flow and heat transfer were numerically investigated. It was observed that the local and averaged heat transfer reduce as the value of the Richardson number and internal Rayleigh number increase. As the value of the elastic modulus of the inclined wall and nanoparticle volume fraction increase, local and average heat transfer enhance. The discrepancy between the averaged Nusselt number increase for different sizes for the lower values of elastic modulus of the flexible wall. When heat transfer process is effective adding nanoparticles to the base fluid is advantageous.

Mixed convection in a partially heated triangular cavity filled with nanofluid having a partially flexible wall and internal heat generation

Natural convection in a flexible sided triangular cavity with internal heat generation under the effect of inclined magnetic field

Mixed convection in a lid-driven cavity containing triangular block with constant heat flux: Effect of location of block

A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows

A spectral method for the triangular cavity flow

Current-topography interactions in the ocean give rise to eddies spanning a wide range of spatial and temporal scales. Latest modeling efforts indicate that coastal and underwater topography are important generation sites for submesoscale coherent vortices (SCVs), characterized by horizontal scales of (0.1 – 10) km. Using idealized, submesoscale and BBL-resolving simulations and adopting an integrated vorticity balance formulation, we quantify precisely the role of bottom boundary layers (BBLs) in the vorticity generation process. In particular, we show that vorticity generation on topographic slopes is attributable primarily to the torque exerted by the vertical divergence of stress at the bottom. We refer to this as the Bottom Stress Divergence Torque (BSDT). BSDT is a fundamentally nonconservative torque that appears as a source term in the integrated vorticity budget and is to be distinguished from the more familiar Bottom Stress Curl (BSC). It is closely connected to the bottom pressure torque (BPT) via the horizontal momentum balance at the bottom and is in fact shown to be the dominant component of BPT in solutions with a well-resolved BBL. This suggests an interpretation of BPT as the sum of a viscous, vorticity generating component (BSDT) and an inviscid, ‘flow-turning ’ component. Companion simulations without bottom drag illustrate that although vorticity generation can still occur through the inviscid mechanisms of vortex stretching and tilting, the wake eddies tend to have weaker circulation, be substantially less energetic, and have smaller spatial scales.

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Boundary-Layer-Mediated Vorticity Generation in Currents over Sloping Bathymetry

Uniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a “blocking level” is s...

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Stratified Flows over and around Long Dynamically Tall Mountain Ridges

Submesoscale coherent vortices (SCVs) are a ubiquitous feature of topographic wakes in the extratropical oceans. Recent studies demonstrate a mechanism wherein high vorticity bottom boundary layers (BBLs) on the slopes of the topography separate (forming shear layers), undergo instabilities, and subsequently merge in the horizontal and align in the vertical to form vertically coherent, columnar, SCVs (i.e. with low vertical shear). Background rotation is critical to the vertical alignment of unstable vortical filaments into coherent SCVs. In the tropics, however, the weakening of rotation prevents this alignment. Employing an idealized framework of steady barotropic flow past an isolated seamount in a background of constant stratification N and rotation rate f, we examine the wake structure for a range of f values spanning values from the poles to the tropics. We find a systematic increase in the interior vertical shear with decreasing f that manifests as a highly layered wake structure consisting of vertically thin, ‘pancake’ SCVs possessing a high vertical shear. A monotonic increase in the wake energy dissipation rate is concomitantly observed with decreasing f. By examining the evolution equations for the vertical shear and vertical enstrophy, we find that the interior shear generation is an advective process, with the location of peak shear generation approximately colocated with maximum energy dissipation. This leads to the inference that high wake dissipation in tropical tropographic wakes is caused by parameterized shear instabilities induced by interior advective generation of vertical shear in the near wake region.

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High Vertical Shear and Dissipation in Equatorial Topographic Wakes

We present in-situ and remote observations of a Mississippi plume front in the Louisiana bight. The plume propagated freely across the bight, rather than as a coastal current. The observed ...

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Arjun Jagannathan

Papers

A spectral method for the triangular cavity flow

Boundary-Layer-Mediated Vorticity Generation in Currents over Sloping Bathymetry

Stratified Flows over and around Long Dynamically Tall Mountain Ridges

High Vertical Shear and Dissipation in Equatorial Topographic Wakes

Observations of Shoaling Density Current Regime Changes in Internal Wave Interactions