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 -10 15 , for Prandtl number Pr = 5 and a small aspect ratio, and show that a sequence of several stability transitions at Ra ∼ 10 10 -10 11 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 ∼ Ra 1/5 . 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 (10 10 < Ra < 10 13 ) reveals that the small scales of motion are produced predominantly by thermal convection, whereas at Ra 10 14 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 ∼ 10 15 .

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 $-1\,^{\circ }\text{C}$ and $6\,^{\circ }\text{C}$ 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.

Three-dimensional direct numerical simulation of horizontal convection is reported for a large Rayleigh number, $\mathit{Ra}\sim O(1{0}^{12} )$, and boundary conditions that allow comparison with previous laboratory experiments. The convection is forced by heating over half of the horizontal base of a long channel and cooling over the other half of the base. The solutions are consistent with the experiments, including small-scale streamwise roll instability developing into a convectively mixed layer within the bottom thermal boundary layer, and a turbulent endwall plume. The mechanical energy budget is shown to be dominated by conversions of available potential energy to kinetic energy by buoyancy flux in the plume and the reverse in the interior of the circulation. These local conversions are three orders of magnitude greater than the total rate of viscous dissipation. The total irreversible mixing is exactly equal to the generation of available potential energy by buoyancy forcing, and one order of magnitude larger than the viscous dissipation. This confirms that dissipation rate is not an indicator of the strength of the circulation and explains why horizontal convection is more energetic than might be expected.

Topography influences the circulation in the Southern Ocean, generating stationary meanders in the lee of topographic features, triggering hot spots of mesoscale eddy kinetic energy, and modifying jets and fronts. However, the relationship between topography and submesoscale flows (with length scales of order 1-10 km) has not yet been explored. The first submesoscale-resolving (1/80• resolution) ocean model, with realistic topography of the Indian sector of the Southern Ocean, is used to investigate this interaction.The results show spatial inhomogeneity in submesoscale activity that is correlated with topography. Topographic influence is primarily indirect: topography controls mesoscale flows, which in turn generate submesoscale activity. Mesoscale eddy kinetic energy and strain rate can be used, to first order, to infer submesoscale vertical velocity, implying a possible route to parameterise submesoscale activity in coarser resolution models.

A numerical study is performed to investigate nonlinear processes during internal wave generation by the oscillation of a background barotropic tide over a sloping bottom. The focus is on the near-critical case where the slope angle is equal to the natural internal wave propagation angle and, consequently, there is a resonant wave response that leads to an intense boundary flow. The resonant wave undergoes both convective and shear instabilities that lead to turbulence with a broad range of scales over the entire slope. A thermal bore is found during upslope flow. Spectra of the baroclinic velocity, both inside the boundary layer and in the external region with free wave propagation, exhibit discrete peaks at the fundamental tidal frequency, higher harmonics of the fundamental, subharmonics and inter-harmonics in addition to a significant continuous part. The internal wave flux and its distribution between the fundamental and harmonics is obtained. Turbulence statistics in the boundary layer including turbulent kinetic energy and dissipation rate are quantified. The slope length is varied with the smaller lengths examined by direct numerical simulation (DNS) and the larger with large-eddy simulation (LES). The peak value of the near-bottom velocity increases with the length of the critical region of the topography. The scaling law that is observed to link the near-bottom peak velocity to slope length is explained by an analytical boundary-layer solution that incorporates an empirically obtained turbulent viscosity. The slope length is also found to have a strong impact on quantities such as the wave energy flux, wave energy spectra, turbulent kinetic energy, turbulent production and turbulent dissipation.