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The Antarctic Ice Sheet is losing mass as a result of increased ocean-driven melting of its fringing ice shelves. Efforts to represent the effects of basal melting in sea level projections are undermined by poor understanding of the turbulent ice shelf–ocean boundary layer (ISOBL), a meters-thick layer of ocean that regulates heat and salt transfer between the ocean and ice. To address this shortcoming, we perform large-eddy simulations of the ISOBL formed by a steady, geostrophic flow beneath horizontal ice. We investigate melting and ISOBL structure and properties over a range of free-stream velocities and ocean temperatures. We find that the melting response to changes in thermal and current forcing is highly nonlinear due to the effects of meltwater on ISOBL turbulence. Three distinct ISOBL regimes emerge depending on the relative strength of current shear and buoyancy forcing: “well-mixed,” “stratified,” or “diffusive-convective.” We present expressions for mixing-layer depth for each regime and show that the transitions between regimes can be predicted with simple nondimensional parameters. We use these results to develop a novel regime diagram for the ISOBL which provides insight into the varied melting responses expected around Antarctica and highlights the need to include stratified and diffusive-convective dynamics in future basal melting parameterizations. We emphasize that melting in the diffusive-convective regime is time dependent and is therefore inherently difficult to parameterize. Significance Statement The purpose of this study is to investigate the processes that control ocean-driven melting of Antarctic ice shelves (100–1000-m-thick floating extensions of the Antarctic ice sheet). Currently, these processes are poorly understood due to the difficulty of accessing the ocean beneath ice shelves. Using an ocean model, we determine the melting response to different ocean conditions, including feedbacks whereby cold, fresh meltwater can enhance or suppress turbulent eddies beneath the ice, depending on the ocean state. Our results point the way to improvements in the representation of ocean-driven melting in ocean/climate models, which will allow more accurate predictions of future climate and sea level.

Eddy-freshwater interaction is studied in the north Bay of Bengal (BoB) with a high-resolution simulation using the Regional Ocean Modeling System. Following observations, the model simulates the trapping and homogenization of river water by a cyclonic mesoscale eddy on a sub-monthly time scale from October-November of 2015. As fresh river water is trapped in the eddy, it is characterized by strong vertical and lateral gradients in salinity. Within a few weeks, these gradients relax along with the progressive homogenization of freshwater within the eddy. A mixed layer salinity budget shows the importance of ageostrophic vertical advection in addition to lateral advection during the evolution of salinity within the eddy. An analysis of the eddy kinetic energy (EKE) budget in the upper ocean indicates the development of barotropic and baroclinic instabilities. The vertical profiles of EKE conversion terms reveal that the surface freshwater was involved in the evolution of baroclinic instability within the mixed layer. In addition, an eddy available potential energy (EPE) budget shows that the entrainment of the river water raises the EPE, which is due to an increase in lateral salinity gradients across the eddy during the trapping event. Subsequently, the salinity homogenization leads to a decrease in the EPE, and its rate of decay is modulated by a correlation between surface buoyancy fluxes and density anomalies. Finally, reanalysis data show similar trapping and homogenization events across multiple years, highlighting the importance of this mechanism of subseasonal freshwater evolution in the BoB., 37 pages, 27 figures, and to be submitted to Journal of Physical Oceanography

Open-ocean convection is a common phenomenon that regulates mixed layer depth and ocean ventilation in the high-latitude oceans. However, many climate model simulations overestimate mixed layer depth during open-ocean convection, resulting in excessive formation of dense water in some regions. The physical processes controlling transient mixed layer depth during open-ocean convection are examined using two different numerical models: a high-resolution, turbulence-resolving nonhydrostatic model and a large-scale hydrostatic ocean model. An isolated destabilizing buoyancy flux is imposed at the surface of both models and a quasi-equilibrium flow is allowed to develop. Mixed layer depth in the turbulence-resolving and large-scale models closely aligns with existing scaling theories. However, the large-scale model has an anomalously deep mixed layer prior to quasi-equilibrium. This transient mixed layer depth bias is a consequence of the lack of resolved turbulent convection in the model, which delays the onset of baroclinic instability. These findings suggest that in order to reduce mixed layer biases in ocean simulations, parameterizations of the connection between baroclinic instability and convection need to be addressed.

Volume transport in the presence of fully resolved convection and turbulence is investigated in a reentrant channel model of the Southern Ocean. The response of the meridional overturning and zonal transport to variations in wind and buoyancy forcing is quantified. Our simulations show two overturning cells—a buoyancy‐driven lower cell and a wind‐driven upper cell. The lower overturning cell is much larger in meridional extent and magnitude than the upper cell. The mean component of the overturning transport is smaller than the fluctuating component in the lower overturning cell, indicating that transport is dominated by eddies and/or turbulent convective flow. In contrast, the upper cell can be primarily described as a mean flow (indicating minimal eddy compensation). Both cells strengthen with increasing winds, with the upper cell being more sensitive to increasing wind intensity than the lower cell. Scaling for the mean upper overturning is also derived and matches previous theories which predict a linear sensitivity of the upper cell to wind. Zonal transport remains insensitive to increasing wind stress, suggesting that the system is eddy saturated when turbulence and eddies are resolved. These results suggest that fine‐scale flows control zonal transport and abyssal meridional overturning in the Southern Ocean, while wind stress drives the upper meridional overturning transport, highlighting the importance of accurately characterizing turbulence and convection in large‐scale models.

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 $Ra\approx 10^{12}{-}10^{13}$). The dynamics are found to depend on the value of a convective Rossby number, $Ro_{\unicode[STIX]{x0394}T}$, which represents the strength of buoyancy forcing relative to Coriolis forces. Vertical convection shifts from a mean endwall plume under weak rotation ($Ro_{\unicode[STIX]{x0394}T}>10^{-1}$) to ‘open ocean’ chimney convection plus mean vertical plumes at the side boundaries under strong rotation ($Ro_{\unicode[STIX]{x0394}T}). 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.

Freshwater from rivers influences Indian summer monsoon rainfall and regional tropical cyclones by shallowing the upper layer and warming the subsurface ocean in the Bay of Bengal. Here, we use in situ and satellite data with reanalysis products to showcase how river water can experience a significant increase in salinity on subseasonal timescales. This involves the trapping and homogenization of freshwater by a cyclonic eddy in the Bay. Specifically, in October 2015, river water is shown to enter a particularly long-lived eddy along with its attracting manifolds within a period of two weeks. The eddy itself is quite unique in that it lasted for 16 months in the Bay where average lifespans are of the order of 2-3 months. This low salinity water results in the formation of a highly stratified surface layer. In fact, when freshest, the eddy has the highest sea-level anomalies, spins fastest, and supports strong lateral gradients in salinity. Subsequently, observations reveal progressive homogenization of salinity and relaxation of sea-level anomalies and salinity gradients within a month. In particular, salty water spirals in, and freshwater is pulled out across the eddy boundary. Lagrangian experiments elucidate this process, whereby horizontal chaotic mixing provides a mechanism for the rapid increase in surface salinity on the order of timescale of a month. This pathway is distinct from vertical mixing and likely to be important in the eddy-rich Bay of Bengal., 11 pages, 11 Figures

Using field, numerical, and laboratory studies, we consider the roles of both shear and convection in driving mixing in the interior of the density-stratified ocean. Shear mixing dominates when the Richardson number Ri 1.0, and in the intermediate regime when 0.25

The Antarctic Ice Sheet loses about half its mass through ocean-driven melting of its fringing ice shelves. However, the ocean processes governing ice shelf melting are not well understood, contributing to uncertainty in projections of Antarctica's contribution to global sea level. We use high-resolution large-eddy simulation to examine ocean-driven melt, in a geophysical-scale model of the turbulent ice shelf-ocean boundary layer, focusing on the ocean conditions observed beneath the Ross Ice Shelf. We quantify the role of double-diffusive convection in determining ice shelf melt rates and oceanic mixed layer properties in relatively warm and low-velocity cavity environments. We demonstrate that double-diffusive convection is the first-order process controlling the melt rate and mixed layer evolution at these flow conditions, even more important than vertical shear due to a mean flow, and is responsible for the step-like temperature and salinity structure, or thermohaline staircase, observed beneath the ice. A robust feature of the multiday simulations is a growing saline diffusive sublayer that drives a time-dependent melt rate. This melt rate is lower than current ice-ocean parameterizations, which consider only shear-controlled turbulent melting, would predict. Our main finding is that double-diffusive convection is an important process beneath ice shelves, yet is currently neglected in ocean-climate models.

The Antarctic Ice Sheet (AIS) is out of equilibrium with the current anthropogenic‐enhanced climate forcing. Paleoenvironmental records and ice sheet models reveal that the AIS has been tightly coupled to the climate system during the past and indicate the potential for accelerated and sustained Antarctic ice mass loss into the future. Modern observations by contrast suggest that the AIS has only just started to respond to climate change in recent decades. The maximum projected sea level contribution from Antarctica to 2100 has increased significantly since the Intergovernmental Panel on Climate Change (IPCC) 5th Assessment Report, although estimates continue to evolve with new observational and theoretical advances. This review brings together recent literature highlighting the progress made on the known processes and feedbacks that influence the stability of the AIS. Reducing the uncertainty in the magnitude and timing of the future sea level response to AIS change requires a multidisciplinary approach that integrates knowledge of the interactions between the ice sheet, solid Earth, atmosphere, and ocean systems and across time scales of days to millennia. We start by reviewing the processes affecting AIS mass change, from atmospheric and oceanic processes acting on short time scales (days to decades), through to ice processes acting on intermediate time scales (decades to centuries) and the response to solid Earth interactions over longer time scales (decades to millennia). We then review the evidence of AIS changes from the Pliocene to the present and consider the projections of global sea level rise and their consequences. We highlight priority research areas required to improve our understanding of the processes and feedbacks governing AIS change.

Midlatitude gyres in the ocean are large‐scale horizontal circulations that are intensified on the western boundary of the ocean, giving rise to currents such as the Gulf Stream. The physical mechanism underlying gyres is widely recognized to involve the curl of the wind stress, which injects potential vorticity into the upper ocean. However, model results have highlighted the role of surface buoyancy fluxes (principally heating and cooling of the ocean surface) in driving circulation and enhancing gyre variability. Here we present two numerical simulations—one in the fully turbulent regime and the second an eddy‐permitting ocean model—which show that gyre‐like circulation can be driven by surface buoyancy fluxes alone. We explore this phenomenon through a combination of modeling and linear theory to highlight that the transport of ocean gyres depends upon surface buoyancy fluxes as well as wind stress.

The effects of the slope of an ice–seawater interface on the mechanisms and rate of ablation of the ice by natural convection are examined using turbulence-resolving simulations. Solutions are obtained for ice slopes $\unicode[STIX]{x1D703}=2^{\circ }{-}90^{\circ }$, at a fixed ambient salinity and temperature, chosen to represent common Antarctic ocean conditions. For laminar boundary layers the ablation rate decreases with height, whereas in the turbulent regime the ablation rate is found to be height independent. The simulated laminar ablation rates scale with $(\sin \unicode[STIX]{x1D703})^{1/4}$, whereas in the turbulent regime it follows a $(\sin \unicode[STIX]{x1D703})^{2/3}$ scaling, both consistent with the theoretical predictions developed here. The reduction in the ablation rate with shallower slopes arises as a result of the development of stable density stratification beneath the ice face, which reduces turbulent buoyancy fluxes to the ice. The turbulent kinetic energy budget of the flow shows that, for very steep slopes, both buoyancy and shear production are drivers of turbulence, whereas for shallower slopes shear production becomes the dominant mechanism for sustaining turbulence in the convective boundary layer.

Mixing efficiency is a measure of the energy lost to mixing compared to that lost to viscous dissipation. In a turbulent stratified fluid the mixing efficiency is often assumed constant at η = 0.2, whereas with convection it takes values closer to 1. The value of mixing efficiency when both stratified shear flow and buoyancy-driven convection are active remains uncertain. We use a series of numerical simulations to determine the mixing efficiency in an idealized Southern Ocean model. The model is energetically closed and fully resolves convection and turbulence such that mixing efficiency can be diagnosed. Mixing efficiency decreases with increasing wind stress but is enhanced by turbulent convection and by large thermal gradients in regions with a strongly stratified thermocline. Using scaling theory and the model results, we predict an overall mixing efficiency for the Southern Ocean that is significantly greater than 0.2 while emphasizing that mixing efficiency is not constant.

The exclusive properties of passive levitation and ultra-low friction surface formation of ferrofluids have been utilized to design a highly efficient wind energy harvester. A novel design of passive ferrofluid levitation wind energy converter has been proposed and laboratory prototype has been developed. The simulation model has been developed using the ANSYS Workbench Maxwell electromagnetic software and validated by the experimental results. In this paper, different approaches such as response surface method (RSM), central composite design (CCD) and artificial neural network (ANN) modelling have been applied to relate the system output power to the input design parameters of the wind energy harvester system. The sensitivity analysis of design parameters and their interactions have been conducted. The CCD and RSM modelling have been applied for predicting the power output from the design parameters for the energy harvester where the design parameters has been optimized for the maximum power output using the genetic algorithm (GA). Also, the RSM modelling is validated by the analysis of variance. As a result, the optimal design parameter combination to produce the highest power output can be identified. The optimization result will be compared with and verified by the prediction result of the ANN model. It is found that within the range of the design parameters, the maximum power output of the wind energy harvester obtained through the RSM with the GA is close to that predicted by the ANN model. The design optimization method can be extended to develop an upscale model of the wind energy harvester for larger power output. The proposed magnetic levitation technology has many more potential applications in sensors and actuators, cooling and mechanical bearings and in health sectors.

Differential heating applied at a single horizontal boundary forces ‘horizontal convection’, even when there is no net heat flux through the boundary. However, almost all studies of horizontal convection have been limited to a special class of problem in which temperature or heat flux differences were applied in only one direction and over the horizontal length of a box (the Rossby problem; Rossby, Deep-Sea Res., vol. 12, 1965, pp. 9–16). These conditions strongly constrain the flow. Here we report laboratory experiments and direct numerical simulations (DNS) extending the results of Griffiths & Gayen (Phys. Rev. Lett., vol. 115, 2015, 204301) for horizontal convection forced by boundary conditions imposed in a two-dimensional periodic array at a horizontal boundary. The experiments use saline and freshwater fluxes at a permeable base with the imposed boundary salinity having a horizontal length scale one quarter of the width of the box. The flow reaches a state in which the net boundary buoyancy flux vanishes and the bulk of the fluid shows an inertial range of turbulence length scales. A regime transition is seen for increasing water depth, from an array of individual coherent plumes on the forcing scale to convection dominated by emergent larger scales of overturning. The DNS explore the analogous thermally forced case with sinusoidal boundary temperature of wavenumber $n=4$, and are used to examine the Rayleigh number ($Ra$) dependence for shallow- and deep-water cases. For shallow water the flow transitions with increasing $Ra$ from laminar to turbulent boundary layer regimes that are familiar from the Rossby problem and which have normalised heat transport scaling as $Nu\sim Ra^{1/5}$ and $Nu\sim (Ra\,Pr)^{1/5}$, with $Nu$ the Nusselt number and $Pr$ the Prandtl number, in this case maintaining a stable array of coherent turbulent plumes. For deep-water and large $Ra$ the laminar scaling transitions to $Nu\sim (Ra\,Pr)^{1/4}$, with the scales of turbulence extending to the dimensions of the box. The $1/4$ power law regime is explained in terms of the momentum of symmetric, inviscid large scales of motion in the interior coupled to diffusive loss of heat through stabilised parts of the boundary layer. The turbulence production is predominantly by shear instability rather than convection, with viscous dissipation distributed throughout the bulk of the fluid. These conditions are not seen in the highly asymmetric flow in the Rossby problem even at Rayleigh numbers up to six orders of magnitude greater than the transition found here. The new inertial interior regime has the rate of supply of available potential energy, and its removal by mixing of density, increasing as $Ra^{5/4}$, which is faster than $Ra^{6/5}$ in the Rossby problem. Irreversible mixing is confined close to the forcing boundary and is very much larger than the viscous dissipation, which is proportional to $Ra$.

Convection in a rotating rectangular basin with differential thermal forcing at one horizontal boundary is examined using laboratory experiments. The experiments have an imposed heat flux boundary condition, are at large values of the flux Rayleigh number ($Ra_{F}\sim O(10^{13}{-}10^{14})$ based on the box length $L$), use water with Prandtl number $Pr\approx 4$ and have a small depth to length aspect ratio. The results show the conditions for transition from non-rotating horizontal convection governed by an inertial–buoyancy balance in the thermal boundary layer, to circulation governed by geostrophic flow in the boundary layer. The geostrophic balance constrains mean flow and reduces the heat transport as Nusselt number $Nu\sim (Ra_{F}Ro)^{1/6}$, where $Ro=B^{1/2}/f^{3/2}L$ is the convective Rossby number, $B$ is the imposed buoyancy flux and $f$ is the Coriolis parameter. Thus flow in the geostrophic boundary layer regime is governed by the relative roles of horizontal convective accelerations and Coriolis accelerations, or buoyancy and rotation, in the boundary layer. Experimental evidence suggests that for more rapid rotation there is another transition to a regime in which the momentum budget is dominated by fluctuating vertical accelerations in a region of vortical plumes, which we refer to as a ‘chimney’ following related discussion of regions of deep convection in the ocean. Coupling of the chimney convection in the region of destabilising boundary flux to the diffusive boundary layer of horizontal convection in the region of stabilising boundary flux gives heat transport independent of rotation in this ‘inertial chimney’ regime, and the new scaling $Nu\sim Ra_{F}^{1/4}$. Scaling analysis predicts the transition conditions observed in the experiments, as well as a further ‘geostrophic chimney’ regime in which the vertical plumes are controlled by local geostrophy. When $Ro, the convection is also observed to produce a set of large basin-scale gyres at all depths in the time-averaged flow.

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

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.

We performed direct numerical simulations to investigate the interaction of a vertical ice interface with seawater, and particularly the small-scale convection generated when a wall of Antarctic ice melts in the salty and warmer seawater. The three coupled interface equations are used, along with the Boussinesq and non-hydrostatic governing equations of motion and equation of state for seawater, to solve for interface temperature, salinity and melt rate. Fluxes of both heat and salt to the interface play significant roles in rate of ice melting. The main focus is on the dissolving of ice (at ambient water temperatures between −1° C and 6° C and salinity around 35 ‰) as characterizes many sites around Antarctica. Under these conditions the diffusion of salt to the ice-waterinterface depresses the freezing point and further enhances heat diffusion to the ice.

A numerical study based on large eddy simulation (LES) is performed to investigate the nonlinear interaction of a semidiurnal (M2) internal wave beam with an upper ocean pycnocline. During refraction through the pycnocline, the wave beam undergoes parametric subharmonic instability (PSI) with formation of waves with (1/2)M2 frequency. The three-dimensional LES enables new results that quantify the route to turbulence through PSI. The subharmonic waves generated from PSI have an order of magnitude smaller vertical scale and are susceptible to wave breaking. Convective instability initiates transition to turbulence, while shear production maintains it. Turbulence at points in the subharmonic wave paths is modulated at (1/2)M2 frequency. The beam suffers substantial degradation owing to PSI, reflected harmonics and ducted waves so that only about 30% of the incoming energy is transported by the main reflected beam.

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,$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}Ra\sim 10^8\mbox{--}10^{15}$, for Prandtl number$Pr=5$and a small aspect ratio, and show that a sequence of several stability transitions at$Ra \sim 10^{10}\mbox{--} 10^{11}$defines a change from laminar to turbulent flow. The Prandtl number dependence too is examined at$Ra = 5.86 \times 10^{11}$. 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$Nu\sim Ra^{1/5}$. 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 ($10^{10}) reveals that the small scales of motion are produced predominantly by thermal convection, whereas at$Ra \ge 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 \sim 10^{15}$.

[1] Numerical simulations are performed to investigate the interaction of a semidiurnal internal wave (IW) beam with the nonuniform stratification of an upper ocean pycnocline. During the initial stage of the interaction, higher harmonics originate after reflection of the IW beam at the caustic and are trapped in the pycnocline. In cases where the pycnocline thickness is sufficiently large (approximately larger than twice the dominant wavelength in the beam), the incoming beam undergoes a parametric subharmonic instability (PSI) during refraction through the pycnocline at later time. Consequently, there is significant energy transfer to subharmonic motions that exhibit exponential growth with a rate of 2/3 day−1. The instability is demonstrated to be a resonant triad interaction by diagnostics in both wave frequency and wave number spaces. Smaller vertical scales originate during the PSI, lead to wave steepening, and produce convective overturns. This work identifies a potential mechanism that drives IW beam degradation during its propagation through the upper ocean.

Direct numerical simulation is performed with a focus on the characterization of nonlinear dynamics during reflection of a plane internal wave at a sloping bottom. The effect of incoming wave amplitude is assessed by varying the incoming Froude number, $Fr$, and the effect of off-criticality is assessed by varying the slope angle in a range of near-critical values. At low $\mathit{Fr}$, the numerical results agree well with linear inviscid theory of near-critical internal wave reflection. With increasing $\mathit{Fr}$, the reflection process becomes nonlinear with the formation of higher harmonics and the initiation of fine-scale turbulence during the evolution of the reflected wave. Later in time, the wave response becomes quasi-steady with a systematic dependence of turbulence on the temporal and spatial phase. Convective instabilities are found to play a crucial role in the formation of turbulence during each cycle. The cycle evolution of flow statistics is studied in detail and qualitative differences between off-critical and critical reflection are identified. The parametric dependence of turbulence levels on Froude number and slope angle is calculated. Interestingly, at a given value of $\mathit{Fr}$, the turbulent kinetic energy (TKE) can be higher for somewhat off-critical reflection compared to exactly critical reflection. For a fixed slope angle, as the Froude number increases in the simulated cases, the fraction of the input wave energy converted into the turbulent kinetic energy and the fraction of the input wave power dissipated by turbulence also increase.

The dynamics of horizontal convection are revealed by examining transient adjustment toward thermal equilibrium. We restrict attention to high Rayleigh numbers (of $O(1{0}^{12} )$) and a Prandtl number ${\sim }5$ that characterize many practical applications, and consider responses to small changes in the thermal boundary conditions, using laboratory experiments, three-dimensional direct numerical simulations (DNS) and simple theoretical models. The experiments and the mechanical energy budget from the DNS demonstrate that unsteady forcing can produce flow dramatically more active than horizontal convection under steady forcing. The physical mechanisms at work are indicated by the time scales of approach to the new equilibrium, and we show that these can range over two orders of magnitude depending on the imposed change in boundary conditions. Changes that lead to a net destabilizing buoyancy flux give rapid adjustments: for applied heat flux conditions the whole of the circulation is controlled by conduction through the stable portion of the boundary layer, whereas for applied temperature difference the circulation is controlled by small-scale convection within the unstable part of the boundary layer. The experiments, DNS and models are in close agreement and show that the time scale under applied temperatures is as small as 0.01 vertical diffusion time scales, a factor of four smaller than for imposed flux. Both cases give adjustments too rapid for diffusion in the interior to play a significant role, at least through 99 % of the adjustment, and we conclude that diffusion through the full depth is not significant in setting the equilibrium state. Boundary changes leading to a net stabilizing buoyancy flux give a very different response, causing the convection to quickly form a shallow circulation cell, followed eventually by a return to full-depth overturning through a combination of penetrative convection and conduction. The time scale again varies by orders of magnitude, depending on the boundary conditions and the location of the imposed boundary perturbation.

Direct and large eddy simulations are performed to study the internal waves generated by the oscillation of a barotropic tide over a model ridge of triangular shape. The objective is to go beyond linear theory and assess the role of nonlinear interactions including turbulence in situations with low tidal excursion number. The criticality parameter, defined as the ratio of the topographic slope to the characteristic slope of the tidal rays, is varied from subcritical to supercritical values. The barotropic tidal forcing is also systematically increased. Numerical results of the energy conversion are compared with linear theory and, in laminar flow at low forcing, they agree well in subcritical and supercritical cases but not at critical slope angle. In critical and supercritical cases with higher forcing, there are convective overturns, turbulence and significant reduction (as much as 25 %) of the radiated wave flux with respect to laminar flow results. Analysis of the baroclinic energy budget and spatial modal analysis are performed to understand the reduction. The near-bottom velocity is intensified at critical angle slope leading to a radiated internal wave beam as well as an upslope bore of cold water with a thermal front. In the critical case, the entire slope has turbulence while, in the supercritical case, turbulence originates near the top of the topography where the slope angle transitions through the critical value. The phase dependence of turbulence within a tidal cycle is examined and found to differ substantially between the ridge slope and the ridge top where the beams from the two sides cross.

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.

A numerical study based on large eddy simulation is performed to investigate a bottom boundary layer under an oscillating tidal current. The focus is on the boundary layer response to an external stratification. The thermal field shows a mixed layer that is separated from the external stratified fluid by a thermocline. The mixed layer grows slowly in time with an oscillatory modulation by the tidal flow. Stratification strongly affects the mean velocity profiles, boundary layer thickness and turbulence levels in the outer region although the effect on the near-bottom unstratified fluid is relatively mild. The turbulence is asymmetric between the accelerating and decelerating stages. The asymmetry is more pronounced with increasing stratification. There is an overshoot of the mean velocity in the outer layer; this jet is linked to the phase asymmetry of the Reynolds shear stress gradient by using the simulation data to examine the mean momentum equation. Depending on the height above the bottom, there is a lag of the maximum turbulent kinetic energy, dissipation and production with respect to the peak external velocity and the value of the lag is found to be influenced by the stratification. Flow instabilities and turbulence in the bottom boundary layer excite internal gravity waves that propagate away into the ambient. Unlike the steady case, the phase lines of the internal waves change direction during the tidal cycle and also from near to far field. The frequency spectrum of the propagating wave field is analysed and found to span a narrow band of frequencies clustered around 45°.

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-Benard 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.

The mechanical energy budget for thermally equilibrated Rayleigh–Bénard convection is developed theoretically, with explicit consideration of the role of available potential energy, this being the form in which all the mechanical energy for the flow is supplied. The analysis allows derivation for the first time of a closed analytical expression relating the rate of mixing in symmetric fully developed convection to the rate at which available potential energy is supplied by the thermal forcing. Only about half this supplied energy is dissipated viscously. The remainder is consumed by mixing acting to homogenize the density field. This finding is expected to apply over a wide range of Rayleigh and Prandtl numbers for which the Nusselt number is significantly greater than unity. Thus convection at large Rayleigh number involves energetically efficient mixing of density variations. In contrast to conventional approaches to Rayleigh–Bénard convection, the dissipation of temperature or density variance is shown not to be of direct relevance to the mechanical energy budget. Thus, explicit recognition of available potential energy as the source of mechanical energy for convection, and of both mixing and viscous dissipation as the sinks of this energy, could be of further use in understanding the physics.

A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra ~ 10(7)-10(13). At Ra < 10(7) small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the large- and small-scale motions. In contrast, at Ra ≥ 10(10) most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%.

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.

Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are used to investigate and quantify the dynamical processes underlying turbulence formed during the generation of an internal wave beam and its subsequent interaction with a realistically stratified upper ocean. As a part of the thesis, a three-dimensional mixed spectral/finite difference code was developed, parallelized, validated and employed to study several geophysical problems relevant to internal tide generation and its nonlinear breaking. The thesis research has four phases. In the first phase, a study of a stratified non- sloping bottom boundary layer under an oscillating tide was completed. The focus is on the boundary layer response to an external stratification based on LES. Flow instabilities and turbulence in the bottom boundary layer are found to excite internal gravity waves that propagate away into the ambient with phase angle varying over the tidal cycle. Subsequent studies as part of the second phase consider a stratified oscillating flow over a sloping bottom wall to mimic the generation of baroclinic internal waves (IW) from the tide-topography interaction at a model continental slope. The DNS study shows transition to turbulence, which is present along the entire extent of the near-critical region of the slope in the regime of low background excursion number and Reynolds number. The transition is found to be initiated by a convective instability, which is closely followed by shear instability. The peak value of the near-bottom velocity is found to increase with increasing 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. As an extension of the second phase, the objective of the third phase work is to numerically model a near-bottom beam with a larger, more realistic width using LES and characterize its turbulence statistics. Maximum turbulent kinetic energy and dissipation rate are found just after the zero velocity point when flow reverses from downslope to upslope motion. The phasing and other characteristics of the turbulent mixing in the present simulations show remarkable similarity with that observed off Kaena Ridge in Hawaii taken during the hawaiian ocean mixing experiment (HOME), and may be explained by the beam-scale convective overturns found here. The objective of the final phase is to understand the interaction process between an IW beam and an upper ocean pycnocline and to further characterize the cascade to small scales in the context of IW beam degradation observed in the ocean

From particle simulations of a sheared frictional granular gas, we show that the Coulomb friction can have dramatic effects on orientational correlation as well as on both the translational and angular velocity distribution functions even in the Boltzmann (dilute) limit. The dependence of orientational correlation on friction coefficient (μ) is found to be nonmonotonic, and the Coulomb friction plays a dual role of enhancing or diminishing the orientational correlation, depending on the value of the tangential restitution coefficient (which characterizes the roughness of particles). From the sticking limit (i.e., with no sliding contact) of rough particles, decreasing the Coulomb friction is found to reduce the density and spatial velocity correlations which, together with diminished orientational correlation for small enough μ, are responsible for the transition from non-gaussian to gaussian distribution functions in the double limit of small friction (μ→0) and nearly elastic particles (e→1). This double limit in fact corresponds to perfectly smooth particles, and hence the maxwellian (gaussian) is indeed a solution of the Boltzmann equation for a frictional granular gas in the limit of elastic collisions and zero Coulomb friction at any roughness. The high-velocity tails of both distribution functions seem to follow stretched exponentials even in the presence of Coulomb friction, and the related velocity exponents deviate strongly from a gaussian with increasing friction.

[1] A numerical study based on large eddy simulation (LES) is performed to investigate near-bottom mixing processes in an internal wave beam over a critical slope. Transition to turbulence from an initial laminar state is followed by mixing events that occur at specific phases. Maximum turbulent kinetic energy and dissipation rate are found just after the zero velocity point when flow reverses from downslope to upslope motion. At this phase, convective instability leads to density overturns that originate in the upper flank of the beam and span the beam width of 60 m. Turbulence originating at the bottom and with smaller vertical extent is also present during the phases of peak upslope and downslope flow when the boundary layer shear is large. The present numerical simulations identify and characterize a process, internal wave beam at a critical slope during generation or after propagation from a nearby generation site, that may lead to the high turbulence levels, modulated at the tidal frequency, that is observed near the bottom in oceanic sites with near-critical topography.

Three-dimensional direct numerical simulations are performed to examine nonlinear processes during the generation of internal tides on a model continental slope. An intense boundary flow is generated in the critical case where the slope angle is equal to the natural internal wave propagation angle. Wave steepening, that drives spanwise wave breaking via convective instability, occurs. Turbulence is present along the entire extent of the near-critical region of the slope. The turbulence is found to have a strong effect on the internal wave beam by distorting its near-slope structure. A complicated wave field with a broadband frequency spectrum is found. This work explains the formation of boundary turbulence during the generation of internal tides in the regime of low excursion numbers.

Three-dimensional direct numerical simulations are performed to model an internal tidal beam at near-critical slope, and the phase dependence of turbulent processes is investigated. Convective instability leads to density overturns that originate in the upper flank of the beam and span the beam width of 6 m during flow reversal from downslope to upslope boundary motion. During this flow reversal event, negative turbulent production is observed signaling energy transfer from velocity fluctuations to the mean flow. In this note, we explain the mechanism underlying negative production.

Based on a micropolar continuum of rough granular particles that takes into account the balance equations for the spin (/rotational) velocity and the spin granular temperature, the linear stability characteristics of an unbounded shear flow ( ${\bm u}\equiv (u_x, u_y, u_z) \,{=}\, (\dot\gamma y, 0, 0)$ , where $x$ , $y$ and $z$ are the streamwise, transverse and spanwise directions, respectively, and $\dot\gamma$ is the shear rate) are analysed. For pure spanwise perturbations ( $k_z\neq 0$ , with $k_x\,{=}\,0\,{=}\,k_y$ , where $k_i$ is the wavenumber in the $i$ th direction), we show that the streamwise translational velocity and the transverse spin velocity modes are subject to linear growths, owing to an inviscid ‘algebraic’ instability (that grows linearly with time). This algebraic instability is shown to be tied to a hidden mechanism of momentum transfer from the translational to the rotational modes, via pure spanwise perturbations to the transverse velocity – in short, we have uncovered an ‘instability-induced rotational-driving’ mechanism. Pure spanwise ( $k_z\neq 0$ , with $k_x\,{=}\,0\,{=}\,k_y$ ) and pure transverse ( $k_y\neq 0$ , with $k_x\,{=}\,0\,{=}\,k_z$ ) perturbations give rise to ‘exponential’ instabilities (that grow exponentially with time) which are related to similar stationary instabilities in the shear flow of smooth, inelastic particles. Both these instabilities also survive in the limiting case of perfectly elastic but rough particles. The scalings of hydrodynamic modes with wavenumbers have been obtained via the respective long-wave expansion. Perturbations with modulations in all three directions are shown to be stable in the asymptotic time limit, but there could be short-time ‘exponential’ growth of these general perturbations in the long-wave limit for both travelling and stationary waves. The growth rate of all instabilities is maximum at intermediate values of the tangential restitution coefficient ( $\beta$ ), and decreases in both the perfectly smooth ( $\beta\to -1$ ) and rough ( $\beta\to 1$ ) limits; the associated instability length scale is minimum at intermediate $\beta$ , and increases in both the perfectly smooth and rough limits. In the perfectly smooth limit, there is a window of particle volume fraction ( $\phi$ ), $\phi_c^s , over which the flow remains stable to all perturbations. With the inclusion of spin fields, the size of this window decreases and at moderate dissipations with $\beta\,{>}\,0.5$ the flow becomes unstable at all $\phi$ .