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Abstract Current eddy‐permitting and eddy‐resolving ocean models require dissipation to prevent a spurious accumulation of enstrophy at the grid scale. We introduce a new numerical scheme for momentum advection in large‐scale ocean models that involves upwinding through a weighted essentially non‐oscillatory (WENO) reconstruction. The new scheme provides implicit dissipation and thereby avoids the need for an additional explicit dissipation that may require calibration of unknown parameters. This approach uses the rotational, “vector invariant” formulation of the momentum advection operator that is widely employed by global general circulation models. A novel formulation of the WENO “smoothness indicators” is key for avoiding excessive numerical dissipation of kinetic energy and enstrophy at grid‐resolved scales. We test the new advection scheme against a standard approach that combines explicit dissipation with a dispersive discretization of the rotational advection operator in two scenarios: (a) two‐dimensional turbulence and (b) three‐dimensional baroclinic equilibration. In both cases, the solutions are stable, free from dispersive artifacts, and achieve increased “effective” resolution compared to other approaches commonly used in ocean models. 

In the problem of horizontal convection a non-uniform buoyancy, $$b_{s}(x,y)$$ , is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $$\boldsymbol{J}$$ , defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $$\overline{\boldsymbol{J}\boldsymbol{\cdot }\unicode[STIX]{x1D735}b_{s}}=-\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ ; the overbar denotes a space–time average over the top surface, angle brackets denote a volume–time average and $$\unicode[STIX]{x1D705}$$ is the molecular diffusivity of buoyancy  $$b$$ . This connection between $$\boldsymbol{J}$$ and $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ justifies the definition of the horizontal-convective Nusselt number, $Nu$ , as the ratio of $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent ‘surface Nusselt number’, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $$b_{s}(x,y)$$ . In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of $$|\unicode[STIX]{x1D735}b|^{2}$$ demanded by $$\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$$ . 

Abstract Arctic icebergs, unconstrained sea ice floes, oil slicks, mangrove drifters, lost cargo containers, and other flotsam are known to move at 2%–4% of the prevailing wind velocity relative to the water, despite vast differences in the material properties, shapes, and sizes of objects. Here, we revisit the roles of density, aspect ratio, and skin and form drag in determining how an object is driven by winds and water currents. Idealized theoretical considerations show that although substantial differences exist for end members of the parameter space (either very thin or thick and very light or dense objects), most realistic cases of floating objects drift at approximately 3% of the free-stream wind velocity (measured outside an object’s surface boundary layer) relative to the water. This relationship, known as a long-standing rule of thumb for the drift of various types of floating objects, arises from the square root of the ratio of the density of air to that of water. We support our theoretical findings with flume experiments using floating objects with a range of densities and shapes. 

Abstract Circulation in the Southern Ocean is unique. The strong wind stress forcing and buoyancy fluxes, in concert with the lack of continental boundaries, conspire to drive the Antarctic Circumpolar Current replete with an intense eddy field. The effect of Southern Ocean eddies on the ocean circulation is significant—they modulate the momentum balance of the zonal flow, and the meridional transport of tracers and mass. The strength of the eddy field is controlled by a combination of forcing (primarily thought to be wind stress) and intrinsic, chaotic, variability associated with the turbulent flow field itself. Here, we present results from an eddy‐permitting ensemble of ocean model simulations to investigate the relative contribution of forced and intrinsic processes in governing the variability of Southern Ocean eddy kinetic energy. We find that variations of the eddy field are mostly random, even on longer (interannual) timescales. Where correlations between the wind stress forcing and the eddy field exist, these interactions are dominated by two distinct timescales—a fast baroclinic instability response; and a multi‐year process owing to feedback between bathymetry and the mean flow. These results suggest that understanding Southern Ocean eddy dynamics and its larger‐scale impacts requires an ensemble approach to eliminate intrinsic variability, and therefore may not yield robust conclusions from observations alone.