A physical–statistical recipe for representation of small-scale oceanic turbulent mixing in climate models

It is well established that small-scale cross-density (diapycnal) turbulent mixing induced by breaking of overturns in the interior of the ocean plays a significant role in sustaining the deep ocean circulation and in regulating tracer budgets such as those of heat, carbon and nutrients. There has been significant progress in the fluid mechanical understanding of the physics of breaking internal waves. Connection of the microphysics of such turbulence to the larger scale dynamics, however, is significantly underdeveloped. We offer a hybrid theoretical–statistical approach, informed by observations, to make such a link. By doing so, we define a bulk flux coefficient, ΓB , which represents the partitioning of energy available to an ‘ocean box’ (such as a grid cell of a coarse resolution climate model), from winds, tides, and other sources, into mixing and dissipation. Here, ΓB depends on both the statistical distribution of turbulent patches and the flux coefficient associated with individual patches, Γi . We rely on recent parametrizations of Γi and the seeming universal characteristics of statistics of turbulent patches to infer ΓB , which is the essential quantity for representation of turbulent diffusivity in climate models. By applying our approach to climatology and global tidal estimates, we show that, on a basin scale, energetic mixing zones exhibit moderately efficient mixing that induces significant vertical density fluxes, while quiet zones (with small background turbulence levels), although highly efficient in mixing, exhibit minimal vertical fluxes. The transition between the less energetic to more energetic zones marks regions of intense upwelling and downwelling of deep waters. We suggest that such upwelling and downwelling may be stronger than previously estimated, which in turn has direct implications for the closure of the deep branch of the ocean meridional overturning circulation as well as for the associated tracer budgets

Impact of spatial variability in zooplankton grazing rates on carbon export flux

The biological carbon pump is a key controller of how much carbon is stored within the global ocean. This pathway is influenced by food web interactions between zooplankton and their prey. In global biogeochemical models, Holling Type functional responses are frequently used to represent grazing interactions. How these responses are parameterized greatly influences biomass and subsequent carbon export estimates. The half-saturation constant, or k value, is central to the Holling functional response. Empirical studies show k can vary over three orders of magnitude, however, this variation is poorly represented in global models. This study derives zooplankton grazing dynamics from remote sensing products of phytoplankton biomass, resulting in global distribution maps of the grazing parameter k. The impact of these spatially varying k values on model skill and carbon export flux estimates is then considered. This study finds large spatial variation in k values across the global ocean, with distinct distributions for micro- and mesozooplankton. High half-saturation constants, which drive slower grazing, are generally associated with areas of high productivity. Grazing rate parameterization is found to be critical in reproducing satellite-derived distributions of small phytoplankton biomass, highlighting the importance of top-down drivers for this size class. Spatially varying grazing dynamics decrease mean total carbon export by >17% compared to globally homogeneous dynamics, with increases in fecal pellet export and decreases in export from algal aggregates. This study highlights the importance of grazing dynamics to both community structure and carbon export, with implications for modeling marine carbon sequestration under future climate scenarios

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

Efficiency of turbulent mixing in the abyssal ocean circulation

Turbulent mixing produced by breaking of internal waves plays an important role in setting the patterns of downwelling and upwelling of deep dense waters and thereby helps sustain the global deep ocean overturning circulation. A key parameter used to characterize turbulent mixing is its efficiency, defined here as the fraction of the energy available to turbulence that is invested in mixing. Efficiency is conventionally approximated by a constant value near one sixth. Here we show that efficiency varies significantly in the abyssal ocean and can be as large as approximately one third in density stratified regions near topographic features. Our results indicate that variations in efficiency exert a first-order control over the rate of overturning of the lower branch of the meridional overturning circulation.EPSRC Programme grant EP/K034529/1 entitled “Mathematical Underpinnings of Stratified Turbulence.

Kelvin-Helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries

The temporal stability of a parallel shear flow of miscible fluid layers of dif- ferent density and viscosity is investigated through a linear stability analysis and direct numerical simulations. The geometry and rheology of this Newto- nian fluid mixing can be viewed as a simplified model of the behavior of mud- flow at the bottom of estuaries for suspension studies. In this study, focus is on the stability and transition to turbulence of an initially laminar configuration. A parametric analysis is performed by varying the values of three control pa- rameters, namely the viscosity ratio, the Richardson and Reynolds numbers, in the case of initially identical thickness of the velocity, density and viscosity profiles. The range of parameters has been chosen so as to mimic a wide variety of real configurations. This study shows that the Kelvin-Helmholtz instability is controlled by the local Reynolds and Richardson numbers of the inflection point. In addition, at moderate Reynolds number, viscosity strat- ification has a strong influence on the onset of instability, the latter being enhanced at high viscosity ratio, while at high Reynolds number, the influ- ence is less pronounced. In all cases, we show that the thickness of the mixing layer (and thus resuspension) is increased by high viscosity stratification, in particular during the non-linear development of the instability and especially pairing processes. This study suggests that mud viscosity has to be taken into account for resuspension parameterizations because of its impact on the inflec- tion point Reynolds number and the viscosity ratio, which are key parameters for shear instabilities

On LEM/LES methodology for two-phase flows

A two-phase subgrid combustion model developed earlier has been evaluated for applicability in large-eddy simulations (LES). Direct Numerical Simulations (DNS) of two-phase isotropic turbulence in the presence of passive, momentum-coupled and vaporizing droplets has been extensively studied to form a base-line database. Current DNS results agree with earlier studies and show that the presence of droplets increase the kinetic energy and dissipation at the small scales. LES for these same cases were also carried out to investigate what modifications are needed to incorporate the small-scale turbulence modifications seen in DNS of two-phase flows. LES subgrid modeling for two-phase mixing within the context of the new subgrid combustion model is also addressed