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Direct numerical simulations are used to investigate the nature of fully resolved small-scale convection and its role in large-scale circulation in a rotating f-plane rectangular basin with imposed surface temperature difference. The large-scale circulation has a horizontal geostrophic component and a deep vertical overturning. This paper focuses on convective circulation with no wind stress, and buoyancy forcing sufficiently strong to ensure turbulent convection within the thermal boundary layer (horizontal Rayleigh numbers Ra ≈ 1012–1013). The dynamics are found to depend on the value of a convective Rossby number, Ro1T , which represents the strength of buoyancy forcing relative to Coriolis forces. Vertical convection shifts from a mean endwall plume under weak rotation (Ro1T > 10−1) to ‘open ocean’ chimney convection plus mean vertical plumes at the side boundaries under strong rotation (Ro1T < 10−1 ). The overall heat throughput, horizontal gyre transport and zonally integrated overturning transport are then consistent with scaling predictions for flow constrained by thermal wind balance in the thermal boundary layer coupled to vertical advection–diffusion balance in the boundary layer. For small Rossby numbers relevant to circulation in an ocean basin, vertical heat transport from the surface layer into the deep interior occurs mostly in ‘open ocean’ chimney convection while most vertical mass transport is against the side boundaries. Both heat throughput and the mean circulation (in geostrophic gyres, boundary currents and overturning) are reduced by geostrophic constraints.

Direct numerical simulations (DNS) are used over a three-dimensional rotating basin under geostrophic rotation, in order to understand the relative roles of buoyancy and wind stress on the heat and mass transport. Our main focus is on the large Rayleigh number regime (Ra, being the measure of buoyancy forcing) which is the order of 1012 to sustain turbulent convection. We also maintained small values of convective Rossby number Ro ~ 0.1 at a fixed Prandtl number, Pr ~ 5 while imposing a meridional wind stress pattern.

Direct Numerical Simulation is performed to study the dissolution/melting process of sloping ice-shelves at fixed ambient salinity and temperature. A series of numerical simulations are carried out over various inclinations of the ice block with the horizontal direction. Both laminar and turbulent flows are simulated over shallower slopes. When the boundary layer is laminar, dissolution-rate varies along the slope-length, which decreases in the upslope direction. Dissolution rate is independent in the upslope direction when the boundary layer becomes turbulent. These results are geophysically relevant and can be developed further towards a better parametrisation scheme for the GCMs to estimate the ice-loss around Antarctica

The relative roles of advective processes and mixing on the temporal adjustment of the meridional overturning circulation are examined, in particular the effects of mixing in either the abyssal or upper ocean. Laboratory experiments with convectively driven overturning and imposed stirring rates show that the circulation adjusts toward an equilibrium state on time scales governed by mixing in the upper boundary layer region but independent of the mixing rate in the bulk of the interior. The equilibrium state of the stratification is dependent only on the rate of mixing in the boundary layer. An idealized high-resolution ocean model shows adjustment (of a two-cell circulation) dominated primarily by the advective ventilation time scale, consistent with a view of the circulation determined by water mass transformation occurring primarily near the surface. Both the experiments and the model results indicate that adjustments of the circulation are controlled by surface buoyancy uptake (or rejection) and that the nonequilibrium circulation is dominated by advective processes, especially if the average abyssal ocean diffusivity is less than 3 × 10−5 m2 s−1.

Turbulent mixing and energy dissipation have important roles in the global circulation but are not resolved by ocean models. We use direct numerical simulations of a geostrophic circulation, resolving turbulence and convection, to examine the rates of dissipation and mixing. As a starting point, we focus on circulation in a rotating rectangular basin forced by a surface temperature difference but no wind stress. Emphasis is on the geostrophic regime for the horizontal circulation, but also on the case of strong buoyancy forcing (large Rayleigh number), which implies a turbulent convective boundary layer. The computed results are consistent with existing scaling theory that predicts dynamics and heat transport dependent on the relative thicknesses of thermal and Ekman boundary layers, hence on the relative roles of buoyancy and rotation. Scaling theory is extended to describe the volume-integrated rate of mixing, which is proportional to heat transport and decreases with increasing rotation rate or decreasing temperature difference. In contrast, viscous dissipation depends crucially on whether the thermal boundary layer is laminar or turbulent, with no direct Coriolis effect on the turbulence unless rotation is extremely strong. For strong forcing, in the geostrophic regime, the mechanical energy input from buoyancy goes primarily into mixing rather than dissipation. For a buoyancy-driven circulation in a basin comparable to the North Atlantic we estimate that the total rate of mixing accounts for over 95% of the mechanical energy supply, implying that buoyancy is an efficient driver of mixing in the oceans.

We investigate the convection and dissolution rate generated when a wall of ice dissolves into seawater under Antarctic Ocean conditions. In direct numerical simulations three coupled interface equations are used to solve for interface temperature, salinity and ablation velocity, along with the boundary layer flow and transport. The main focus is on ambient water temperatures between −1∘C and 6∘C and salinities around 35 ‰, where diffusion of salt to the ice–water interface depresses the freezing point and enhances heat diffusion to the ice. We show that fluxes of both heat and salt to the interface are significant in governing the dissolution of ice, and the ablation velocity agrees well with experiments and a recent theoretical prediction. The same turbulent flow dynamics and ablation rate are expected to apply at any depth in a deeper ocean water column (after choosing the relevant pressure coefficient for the liquidus temperature). At Grashof numbers currently accessible by direct numerical simulation, turbulence is generated both directly from buoyancy flux and from shear production in the buoyancy-driven boundary layer flow, whereas shear production by the convective flow is expected to be more important at geophysical scales. The momentum balance in the boundary layer is dominated by buoyancy forcing and wall stress, with the latter characterised by a large drag coefficient.

A large-scale circulation, a turbulent boundary layer, and a turbulent plume are noted features of convection at large Rayleigh numbers under differential heating on a single horizontal boundary. These might be attributed to the forcing, which in all studies has been limited to a unidirectional gradient over the domain scale. We instead apply forcing on a length scale smaller than the domain, and with variation in both horizontal directions. Direct numerical simulations show turbulence throughout the domain, a regime transition to a dominant domain-scale circulation, and a region of logarithmic velocity in the boundary layer, despite zero net heat flux. The results show significant similarities to Rayleigh-Bénard convection, demonstrate the significance of plume merging, support the hypothesis that the key driver of convection is the production of available potential energy without necessarily supplying total potential energy, and imply that contributions to domain-scale circulation in the oceans need not be solely from the large-scale gradients of forcing.

We examine the effect of rotation on horizontal convection using laboratory experiments in a rectangular box domain. Horizontal convection is a basic model for the meridional overturning circulation (MOC) in the ocean; we also expect the MOC is influenced by the Earth's rotation. The Rayleigh number is two orders of magnitude larger than any previous study (Ra ~ 1012) to ensure the flow lies in a regime with a turbulent boundary layer and endwall plume (to better match realistic ocean conditions). Other governing parameters are the Prandtl number Pr ~ 5, aspect ratios AH = 0.16 and AW = 0.24, and Rossby number Ro ~ 0.001-0.1. Particle tracking velocimetry is used to measure horizontal velocity fields at three interior depths, away from the boundary layer that forms adjacent to the thermal forcing. With increasing rotation, the steady state time-averaged flow dynamics changes from a full length cyclonic gyre, to a series of five counter-rotating baroclinic eddies (at non-dimensional Rossby deformation scale of O(1)) and then to a large anticyclonic gyre. The large scale horizontal flow dynamics are largely independent of depth. The divergence and vorticity of the horizontal velocity fields are used to estimate the overturning, which consistently decreases with increases in rotation. Direct Numerical Simulations are ongoing, and will allow access to the energetics of this complicated system.

The MgO content of the highest MgO plume-related komatiites and picrites remained constant at 32 ± 2.5% between 3.5 and 2.7 Ga, then fell to 21 ± 3% by ca. 2.0 Ga, a value similar to the present day value. Because there is a linear relationship between

Recent results have shown that convection forced by a temperature gradient along one horizontal boundary of a rectangular domain at a large Rayleigh number can be turbulent in parts of the flow field. However, the conditions for onset of turbulence, the dependence of flow and heat transport on Rayleigh number, and the roles of large and small scales in the flow, have not been established. We use three-dimensional direct numerical simulation (DNS) and large-eddy simulation (LES) over a wide range of Rayleigh numbers, Ra ~ 10 8-1015, for Prandtl number Pr = 5 and a small aspect ratio, and show that a sequence of several stability transitions at Ra ~ 10 10 - 1011 defines a change from laminar to turbulent flow. The Prandtl number dependence too is examined at Ra = 5.86 × 10 11. At the smallest Ra considered the thermal boundary layer is characterized by a balance of viscous stress and buoyancy, whereas inertia and buoyancy dominate in the large-Ra regime. The change in the momentum balance is accompanied by turbulent enhancement of the overall heat transfer, although both laminar and turbulent regimes give Nu ~ Ra1/5. The results support both viscous and inviscid theoretical scaling models from previous work. The mechanical energy budget for an intermediate range of Rayleigh numbers above onset of instability (1010 < Ra < 1013) reveals that the small scales of motion are produced predominantly by thermal convection, whereas at Ra ≥ 1014 shear instability of the large-scale flow begins to play a dominant role in sustaining the small-scale turbulence. Extrapolation to ocean conditions requires knowledge of the inertial regime identified here, but the simulations show that the corresponding asymptotic balance has not been fully realized by Ra ~ 1015.

Determining the energy budget of the oceans requires evaluating the rates of available potential energy conversion in the circulation. Calculating these conversion rates depends upon the definition of an appropriate "reference" state of the density field, but this definition is complicated in the oceans by the presence of bottom topography. The trapping of dense fluid by topographic barriers means that there are multiple definitions for the reference state. The approach taken in this paper is to examine the sensitivity of the available potential energy budget to several methods for defining the reference state. The first method makes allowances for restrictions imposed on the flow by topography, however it is computationally intensive. The second method is proposed as an inexpensive alternative to the first. These new methods are used to evaluate the energy budget of a model overturning circulation maintained by surface buoyancy forcing. The results are compared with those obtained from two existing methods; one which employs an adiabatic resorting procedure ignoring topography, and one which uses a reference profile developed from the horizontal average of the density field. In our model, the rates of available potential energy conversion are insensitive to the reference state definition providing the reference state is developed from an adiabatic resorting of the domain. These results suggest that any of the adiabatic resorting methods proposed here would be sufficient to evaluate the rates of energy conversion in the ocean.

Mantle plume behavior near subducting plates is still poorly understood and in fact varies significantly from the classical hotspot model. We investigate using 3D laboratory models how subduction-driven flow relates to the deformation and dispersal of a nearby plume. Results show slab-driven flow severely distorts plume-driven flow, entraining and passively advecting plume material despite its thermal buoyancy. Downdip sinking of the slab initially stalls vertical plume ascent while the combination of downdip and rollback sinking motions redistribute material throughout the system. As a consequence of the subduction-induced flow, surface expressions differ significantly from traditional plume expectations. Variations in slab sinking style and plume position lead to a range in head and conduit melting signatures, as well as migrating hotspots. For the Samoa-Tonga system, model predictions are consistent with proposed entrainment of plume material around the subducting plate.