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Jörn Callies and Raffaele Ferrari

Abstract

Baroclinic mixed-layer instabilities have recently been recognized as an important source of submesoscale energy in deep winter mixed layers. While the focus has so far been on the balanced dynamics of these instabilities, they occur in and depend on an environment shaped by atmospherically forced small-scale turbulence. In this study, idealized numerical simulations are presented that allow the development of both baroclinic instability and convective small-scale turbulence, with simple control over the relative strength. If the convection is only weakly forced, baroclinic instability restratifies the layer and shuts off convection, as expected. With increased forcing, however, it is found that baroclinic instabilities are remarkably resilient to the presence of convection. Even if the instability is too weak to restratify the layer and shut off convection, the instability still grows in the convecting environment and generates baroclinic eddies and fronts. This suggests that despite the vigorous atmospherically forced small-scale turbulence in winter mixed layers, baroclinic instabilities can persistently grow, generate balanced submesoscale turbulence, and modify the bulk properties of the upper ocean.

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Malte Jansen and Raffaele Ferrari

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Observations suggest that the time- and zonal-mean state of the extratropical atmosphere adjusts itself such that the so-called “criticality parameter” (which relates the vertical stratification to the horizontal temperature gradient) is close to one. T. Schneider has argued that the criticality parameter is kept near one by a constraint on the zonal momentum budget in primitive equations. The constraint relies on a diffusive closure for the eddy flux of potential vorticity (PV) with an eddy diffusivity that is approximately constant in the vertical.

The diffusive closure for the eddy PV flux, however, depends crucially on the definition of averages along isentropes that intersect the surface. It is argued that the definition favored by Schneider results in eddy PV fluxes whose physical interpretation is unclear and that do not satisfy the proposed closure in numerical simulations. An alternative definition, first proposed by T.-Y. Koh and R. A. Plumb, is preferred. A diffusive closure for the eddy PV flux under this definition is supported by analysis of the PV variance budget and can be used to close the near-surface zonal momentum budget in idealized numerical simulations. Following this approach, it is shown that O(1) criticalities are obtained if the eddy diffusivity decays from its surface value to about zero over the depth of the troposphere, which is likely to be the case in Earth’s atmosphere. Large criticality parameters, however, are possible if the eddy diffusivity decays only weakly in the vertical, consistent with results from quasigeostrophic models. This provides theoretical support for recent numerical studies that have found supercritical mean states in primitive equation models.

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Raffaele Ferrari and Paola Cessi

Abstract

The signatures of feedback between the atmosphere and the ocean are studied with a simple coupled model. The atmospheric component, based on Lorenz's 1984 model is chaotic and has intrinsic variability at all timescales. The oceanic component models the wind-driven circulation, and has intrinsic variability only in the decadal band. The phase of the cospectrum of atmospheric and oceanic temperatures is examined and it is found that in the decadal band, the oceanic signal leads the atmospheric one, while the opposite is true at shorter and longer timescales. The associated atmosphere-only model, driven by the oceanic temperature derived from a coupled run, synchronizes to the coupled run for arbitrary initial conditions. When noise is introduced in the time series of oceanic driving, episodic synchronization still occurs, but only in summer, indicating that control of the atmosphere by the oceanic variables is prevalent in this season.

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Malte Jansen and Raffaele Ferrari

Abstract

A major question for climate studies is to quantify the role of turbulent eddy fluxes in maintaining the observed atmospheric mean state. Both the equator-to-pole temperature gradient and the static stability of the extratropical atmosphere are set by a balance between these eddy fluxes and the radiative forcing. Much attention has been paid to the adjustment of the isentropic slope, which relates the static stability and the meridional temperature gradient. It is often argued that the extratropical atmosphere always equilibrates such that isentropes leaving the surface in the subtropics reach the tropopause near the poles. However, recent work challenged this argument. This paper revisits scaling arguments for the equilibrated mean state of a dry atmosphere, which results from a balance between the radiative forcing and the along-isentropic eddy heat flux. These arguments predict weak sensitivity of the isentropic slope to changes in the radiative forcing, consistent with previous results. Large changes can, however, be achieved if other external parameters, such as the size and rotation rate of the planet, are varied. The arguments are also extended to predict both the meridional temperature gradient and the static stability independently. This allows a full characterization of the atmospheric mean state as a function of external parameters.

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Maxim Nikurashin and Raffaele Ferrari

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Observations and inverse models suggest that small-scale turbulent mixing is enhanced in the Southern Ocean in regions above rough topography. The enhancement extends O(1) km above the topography, suggesting that mixing is supported by the breaking of gravity waves radiated from the ocean bottom. In this study, it is shown that the observed mixing rates can be sustained by internal waves generated by geostrophic motions flowing over bottom topography. Weakly nonlinear theory is used to describe the internal wave generation and the feedback of the waves on the zonally averaged flow. Vigorous inertial oscillations are driven at the ocean bottom by waves generated at steep topography. The wave radiation and dissipation at equilibrium is therefore the result of both geostrophic flow and inertial oscillations differing substantially from the classical lee-wave problem. The theoretical predictions are tested versus two-dimensional high-resolution numerical simulations with parameters representative of Drake Passage. This work suggests that mixing in Drake Passage can be supported by geostrophic motions impinging on rough topography rather than by barotropic tidal motions, as is commonly assumed.

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Maxim Nikurashin and Raffaele Ferrari

Abstract

Recent estimates from observations and inverse models indicate that turbulent mixing associated with internal wave breaking is enhanced above rough topography in the Southern Ocean. In most regions of the ocean, abyssal mixing has been primarily associated with radiation and breaking of internal tides. In this study, it is shown that abyssal mixing in the Southern Ocean can be sustained by internal waves generated by geostrophic motions that dominate abyssal flows in this region. Theory and fully nonlinear numerical simulations are used to estimate the internal wave radiation and dissipation from lowered acoustic Doppler current profiler (LADCP), CTD, and topography data from two regions in the Southern Ocean: Drake Passage and the southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation previously inferred from finescale measurements in the region, suggesting that it is one of the primary drivers of abyssal mixing in the Southern Ocean.

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Raffaele Ferrari and Francesco Paparella

Abstract

The surface mixed layer of the ocean is often characterized by thermohaline compensation and alignment. That is, temperature and salinity gradients tend to be parallel and to cancel in their contribution to density. In this paper a combination of theoretical arguments and numerical simulations is presented to investigate how compensation and alignment emerge as a result of processes at work within the mixed layer. The dynamics of the mixed layer is investigated through a simple model that couples a nonlinear diffusive parameterization for the horizontal transports of temperature and salinity with stirring by mesoscale eddies. It is found that stirring quickly aligns the temperature and salinity gradients and that nonlinear diffusion creates compensation. Neither process, by itself, is sufficient to reproduce the observations.

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Raffaele Ferrari and Maxim Nikurashin

Abstract

Geostrophic eddies control the meridional mixing of heat, carbon, and other climatically important tracers in the Southern Ocean. The rate of eddy mixing is typically quantified through an eddy diffusivity. There is an ongoing debate as to whether eddy mixing in enhanced in the core of the Antarctic Circumpolar Current or on its flanks. A simple expression is derived that predicts the rate of eddy mixing, that is, the eddy diffusivity, as a function of eddy and mean current statistics. This novel expression predicts suppression of the cross-jet eddy diffusivity in the core of the Antarctic Circumpolar Current, despite enhanced values of eddy kinetic energy. The expression is qualitatively and quantitatively validated by independent estimates of eddy mixing from altimetry observations. This work suggests that the meridional eddy diffusivity across the Antarctic Circumpolar Current is weaker than presently assumed because of the suppression of eddy mixing by the strong zonal current.

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Kurt Polzin and Raffaele Ferrari

Abstract

Finescale velocity and density fluctuations consist of both internal waves and vorticity-containing perturbations (vortical modes). A recent decomposition of observations obtained as part of the North Atlantic Tracer Release Experiment (NATRE) permits one to investigate isopycnal stirring associated with vortical modes. This stirring is treated here as a relative dispersion problem in the context of 2D turbulence. Isopycnal diffusivities attain values on the order of 1 m2 s−1 after an initial transient of 5–10 days. After 2 weeks, a patch of tracer with initial radius of 25 m is predicted to have evolved into a convoluted web having an rms radius of 2–4 km. These estimates agree with observations of the evolution of an anthropogenic tracer in NATRE.

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Jörn Callies and Raffaele Ferrari

Abstract

This paper revisits how the restratifying buoyancy flux generated by baroclinic mixed layer instabilities depends on environmental conditions. The frontal spindown is shown to produce buoyancy fluxes that increase significantly beyond the previously proposed and widely used scaling (f is the Coriolis parameter, Λ is the geostrophic shear, and H is the mixed layer depth), irrespective of whether the initial front is broad or narrow. This increase occurs after the initial phase of the nonlinear evolution, when the baroclinic eddies grow in size and develop velocities significantly in excess of the scaling assumption V ~ ΛH. Implications for parameterizing the restratification caused by baroclinic mixed layer instabilities in coarse-resolution models are discussed.

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