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The North Atlantic Ocean circulation, fueled by winds and surface buoyancy fluxes, carries 1.25$\,$PettaWatts of heat poleward in the subtropics, and plays an important role in regulating global weather and climate patterns. Using a series of simulations with perturbed surface forcing, we study how winds and surface heat flux gradients affect the Atlantic meridional heat transport. We decompose the Atlantic meridional heat transport into contributions from circulation cells at warm and cold temperatures (resembling a subtropical gyre and the dense overturning circulation respectively), and a mixed circulation that contains water masses traversing both these cells. Variations in wind stress initially alter the amount of heat carried by the warm and mixed cells, but on long time scales ($>$10 years), changes in the temperature distribution restore the heat transport to equilibrium. Changes in surface buoyancy forcing control the cold cell's circulation, and its associated meridional heat transport, through high-latitude processes., Comment: 14 pages, 3 figures, submitted to the Geophysical Research Letters

When turbulent flow is laden with negatively buoyant particles, their mean distribution over the direction of gravity can induce stable density gradients that penalize turbulent fluctuations. This effect is studied numerically for shear-driven flow with dilute non-inertial sediment. The turbulent dynamics and sediment transport depend critically on particle settling velocity $v_s$, splitting into two regimes: homogeneous weakly stratified turbulence and flow with developed turbulence atop an intermittent boundary layer. At intermediate $v_s$, neither state can be sustained and the flow laminarizes., Comment: 5 pages, 5 figures

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include geometric corrections that account for large variations in slope angle. These are often non-negligible for Earth-surface flows and may consequently be important for simulating natural hazards. We also show how to adapt existing finite volume schemes for the classical shallow water equations, to simulate our new equations in a way that preserves uniform steady states and exactly conserves the combined mass of the flow and bed. Finally, to demonstrate our formulation, we present computations using simple example model closures, fed by point flux sources. On initially constant slopes, flows exhibit different behaviours depending on the grade. Shallow slopes lead to weakly morphodynamic spreading flows that agree well with analytical similarity solutions. On more severe slopes, rapid erosion occurs, leading to self-channelising flows and ultimately a 'super-erosive' state, in which sediment entrainment and gravitational acceleration perpetually reinforce each other., Comment: 28 pages, 8 figures, 1 table

The structure of the Antarctic Slope Current at the continental shelf is crucial in governing the poleward transport of warm water. Canyons on the continental slope may provide a pathway for warm water to cross the slope current and intrude onto the continental shelf underneath ice shelves, which can increase rates of ice shelf melting, leading to reduced buttressing of ice shelves, accelerating glacial flow and hence increased sea level rise. Observations and modelling studies of the Antarctic Slope Current and cross-shelf warm water intrusions are limited, particularly in the East Antarctica region. To explore this topic, an idealised configuration of the Antarctic Slope Current is developed, using an eddy-resolving isopycnal model that emulates the dynamics and topography of the East Antarctic sector. Warm water intrusions via canyons are found to occur in discrete episodes of large onshore flow induced by eddies, even in the absence of any temporal variability in external forcings, demonstrating the intrinsic nature of these intrusions to the slope current system. Canyon width is found to play a key role in modulating cross-shelf exchanges; warm water transport through narrower canyons is more irregular than transport through wider canyons. The intrinsically episodic cross-shelf transport is found to be driven by feedbacks between wind energy input and eddy generation in the Antarctic Slope Current. Improved understanding of the intrinsic variability of warm water intrusions can help guide future observational and modelling studies in the analysis of eddy impacts on Antarctic shelf circulation.

Gyres are central features of large-scale ocean circulation and are involved in transporting tracers such as heat, nutrients, and carbon-dioxide within and across ocean basins. Traditionally, the gyre circulation is thought to be driven by surface winds and quantified via Sverdrup balance, but it has been proposed that surface buoyancy fluxes may also contribute to gyre forcing. Through a series of eddy-permitting global ocean model simulations with perturbed surface forcing, the relative contribution of wind stress and surface heat flux forcing to the large-scale ocean circulation is investigated, focusing on the subtropical gyres. In addition to gyre strength being linearly proportional to wind stress, it is shown that the gyre circulation is strongly impacted by variations in the surface heat flux (specifically, its meridional gradient) through a rearrangement of the ocean's buoyancy structure. On shorter timescales ($\sim$ decade), the gyre circulation anomalies are proportional to the magnitude of the surface heat flux gradient perturbation, with up to $\sim 0.15\,\mathrm{Sv}$ anomaly induced per $\mathrm{W}\,\mathrm{m}^{-2}$ change in the surface heat flux. On timescales longer than a decade, the gyre response to surface buoyancy flux gradient perturbations becomes non-linear as ocean circulation anomalies feed back onto the buoyancy structure induced by the surface buoyancy fluxes. These interactions complicate the development of a buoyancy-driven theory for the gyres to complement the Sverdrup relation. The flux-forced simulations underscore the importance of surface buoyancy forcing in steering the large-scale ocean circulation., Comment: Submitted to the Journal of Physical Oceanography

The collision of a gravitationally-driven horizontal current with a barrier following release from a confining lock is investigated using a shallow water model of the motion, together with a sophisticated boundary condition capturing the local interaction. The boundary condition permits several overtopping modes: supercritical, subcritical, and blocked flow. The model is analysed both mathematically and numerically to reveal aspects of the unsteady motion and to compute the proportion of the fluid trapped upstream of the barrier. Several problems are treated. Firstly, the idealised problem of a uniform incident current is analysed to classify the unsteady dynamical regimes. Then, the extreme regimes of a very close or distant barrier are tackled, showing the progression of the interaction through the overtopping modes. Next, the trapped volume of fluid at late times is investigated numerically, demonstrating regimes in which the volume is determined purely by volumetric considerations, and others where transient inertial effects are significant. For a Boussinesq gravity current, even when the volume of the confined region behind the barrier is equal to the fluid volume, $30\%$ of the fluid escapes the domain, and a confined volume $3$ times larger is required for the overtopped volume to be negligible. For a subaerial dam-break flow, the proportion that escapes is in excess of $60\%$ when the confined volume equals the fluid volume, and a barrier as tall as the initial release is required for negligible overtopping. Finally, we compare our predictions to experiments, showing a good agreement across a range of parameters., Comment: 28 pages, 16 figures, preprint

We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term. This approach incorporates many flow rheologies into a single setting and enables us to investigate the features that set different systems apart. We derive simple formulae for the onset of linear instability, the corresponding linear growth rates and related properties including the existence of monoclinal waves, development of shocks and whether instability is initially triggered up- or downstream of the wave front. Also included within our framework is the presence of shear in the flow velocity profile, which is often neglected in depth-averaged studies. We find that it can significantly modify the threshold for instability. Constant corrections to the governing equations to account for sheared profiles via a 'momentum shape factor' act to stabilize traveling waves. More general correction terms are found to have a nontrivial and potentially important quantitative effect on the properties explored. Finally, we have investigated the spatial properties of the dominant (fastest growing) linear modes. We derive equations for their amplitude and frequency and find that both features can become severely amplified near the front of the traveling wave. For flood waves that propagate into a dry downstream region, this amplification is unbounded in the limit of high disturbance frequency. We show that the rate of divergence is a function of the spatial dependence of the wave depth profile at the front, which may be determined straightforwardly from the drag law., Comment: 27 pages, 9 figures

Atmosphere and ocean are coupled via air-sea interactions. The atmospheric conditions fuel the ocean circulation and its variability, but the extent to which ocean processes can affect the atmosphere at decadal time scales remains unclear. In particular, such low-frequency variability is difficult to extract from the short observational record, meaning that climate models are the primary tools deployed to resolve this question. Here, we assess how the ocean's intrinsic variability leads to patterns of upper-ocean heat content that vary at decadal time scales. These patterns have the potential to feed back on the atmosphere and thereby affect climate modes of variability, such as El Ni\~no or the Interdecadal Pacific Oscillation. We use the output from a global ocean-sea ice circulation model at three different horizontal resolutions, each driven by the same atmospheric reanalysis. To disentangle the variability of the ocean's direct response to atmospheric forcing from the variability due to intrinsic ocean dynamics, we compare model runs driven with inter-annually varying forcing (1958-2018) and model runs driven with repeat-year forcing. Models with coarse resolution that rely on eddy parameterizations, show (i) significantly reduced variance of the upper-ocean heat content at decadal time scales and (ii) differences in the spatial patterns of low-frequency variability compared with higher resolution models. Climate projections are typically done with general circulation models with coarse-resolution ocean components. Therefore, these biases affect our ability to predict decadal climate modes of variability and, in turn, hinder climate projections. Our results suggest that for improving climate projections, the community should move towards coupled climate models with higher oceanic resolution.

It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability properties of these systems in considerable generality. Naive formulations of the morphodynamics, featuring exchange of sediment between a well-mixed suspended load and the bed, lead to mathematically ill-posed governing equations. This is traced to a singularity in the linearised system at Froude number $Fr = 1$ that causes unbounded unstable growth of short-wavelength disturbances. The inclusion of neglected physical processes can restore well posedness. Turbulent momentum diffusion (eddy viscosity) and a suitably parametrised bed load sediment transport are shown separately to be sufficient in this regard. However, we demonstrate that such models typically inherit an associated instability that is absent from non-morphodynamic settings. Implications of our analyses are considered for simple generic closures, including a drag law that switches between fluid and granular behaviour, depending on the sediment concentration. Steady morphodynamic flows bifurcate into two states: dilute flows, which are stable at low $Fr$, and concentrated flows which are always unstable to disturbances in concentration. By computing the growth rates of linear modes across a wide region of parameter space, we examine in detail the effects of specific model parameters including the choices of sediment erodibility, eddy viscosity and bed load flux. These analyses may be used to inform the ongoing development of operational models in engineering and geosciences., Comment: 38 pages, 13 figures

"Eddy saturation" is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic mechanism that involves the competition of sloping isopycnals and restratification by production of baroclinic eddies, and (ii) the barotropic mechanism, that involves production of eddies through lateral shear instabilities or through the interaction of the barotropic current with bathymetric features. Our results suggest that the barotropic flow-component plays a crucial role in determining the total volume transport., Comment: 13 pages, 4 figures

The mesoscale eddy field plays a key role in the mixing and transport of physical and biological properties and redistribute energy budgets in the ocean. Eddy kinetic energy is commonly defined as the kinetic energy of the time-varying component of the velocity field. However, this definition contains all processes that vary in time, including coherent mesoscale eddies, jets, waves, and large-scale motions. The focus of this paper is on the eddy kinetic energy contained in coherent mesoscale eddies. We present a new method to decompose eddy kinetic energy into oceanic processes. The proposed method uses a new eddy-identification algorithm (TrackEddy). This algorithm is based on the premise that the sea level signature of a coherent eddy can be approximated as a Gaussian feature. The eddy Gaussian signature then allows for the calculation of kinetic energy of the eddy field through the geostrophic approximation. TrackEddy has been validated using synthetic sea surface height data, and then used to investigate trends of eddy kinetic energy in the Southern Ocean using Satellite Sea Surface Height anomaly (AVISO+). We detect an increasing trend of eddy kinetic energy associated with mesoscale eddies in the Southern Ocean. This trend is correlated with an increase of the coherent eddy amplitude and the strengthening of wind stress over the last two decades., Comment: 20 pages, 8 figures; TrackEddy available at https://github.com/josuemtzmo/trackeddy

We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the conservation of mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly described by shape factors in the integral equations; the commonly-assumed top-hat profiles lead to shape factors equal to unity. The resultant model is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity, differs from unity. The solutions of the model when source conditions are maintained at constant values retain the form of the well-established steady plume solutions. We demonstrate that the inclusion of a momentum shape factor that differs from unity leads to a well-posed integral model. Therefore, our model does not exhibit the mathematical pathologies that appear in previously proposed unsteady integral models of turbulent plumes. A stability threshold for the value of the shape factor is identified, resulting in a range of its values where the amplitude of small perturbations to the steady solutions decay with distance from the source. The hyperbolic character of the system allows the formation of discontinuities in the fields describing the plume properties during the unsteady evolution. We compute numerical solutions to illustrate the transient development following an abrupt change in the source conditions. The adjustment to the new source conditions occurs through the propagation of a pulse of fluid through the plume. The dynamics of this pulse are described by a similarity solution and, by constructing this new similarity solution, we identify three regimes in which the evolution of the transient pulse following adjustment of the source qualitatively differ., Comment: 41 pages, 16 figures, under consideration for publication in Journal of Fluid Mechanics