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Jörn Callies

Abstract

For small-scale turbulence to achieve water mass transformation and thus affect the large-scale overturning circulation, it must occur in stratified water. Observations show that abyssal turbulence is strongly enhanced in the bottom few hundred meters in regions with rough topography, and it is thought that these abyssal mixing layers are crucial for closing and shaping the overturning circulation. If it were left unopposed, however, bottom-intensified turbulence would mix away the observed mixing-layer stratification over the course of a few years. It is proposed here that the homogenizing tendency of mixing may be balanced by baroclinic restratification. It is shown that bottom-intensified mixing, if it occurs on a large-scale topographic slope such as a midocean ridge flank, not only erodes stratification but also tilts isopycnals in the bottom few hundred meters. This tilting of isopycnals generates a reservoir of potential energy that can be tapped into by submesoscale baroclinic eddies. The eddies slide dense water under light water and thus restratify the mixing layer, similar to what happens in the surface mixed layer. This restratification is shown to be effective enough to balance the homogenizing tendency of mixing and to maintain the observed mixing-layer stratification. This suggests that submesoscale baroclinic eddies may play a crucial role in providing the stratification mixing can act on, thus allowing sustained water mass transformation. Through their restratification of abyssal mixing layers, submesoscale eddies may therefore directly affect the strength and structure of the abyssal overturning circulation.

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Jörn Callies and Raffaele Ferrari

Abstract

The large-scale circulation of the abyssal ocean is enabled by small-scale diapycnal mixing, which observations suggest is strongly enhanced toward the ocean bottom, where the breaking of internal tides and lee waves is most vigorous. As discussed recently, bottom-intensified mixing induces a pattern of near-bottom up- and downwelling that is quite different from the traditionally assumed widespread upwelling. Here the consequences of bottom-intensified mixing for the horizontal circulation of the abyssal ocean are explored by considering planetary geostrophic dynamics in an idealized “bathtub geometry.” Up- and downwelling layers develop on bottom slopes as expected, and these layers are well described by boundary layer theory. The basin-scale circulation is driven by flows in and out of these boundary layers at the base of the sloping topography, which creates primarily zonal currents in the interior and a net meridional exchange along western boundaries. The rate of the net overturning is controlled by the up- and downslope transports in boundary layers on slopes and can be predicted with boundary layer theory.

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Jörn Callies and Weiguang Wu

Abstract

In anticipation of the Surface Water and Ocean Topography (SWOT) wide-swath altimetry mission, this study reviews expectations for sea surface height (SSH) variance spectra at wavelengths of 10–100 km. Kinetic energy spectra from in situ observations and numerical simulations indicate that SSH variance spectra associated with balanced flow drop off steeply with wavenumber, with at least the negative fourth power of the wavenumber. Such a steep drop-off implies that even drastic reductions in altimetry noise yield only a modest improvement in the resolution of balanced flow. This general expectation is made concrete by extrapolating SSH variance spectra from existing altimetry to submesoscales, the results of which suggest that in the extratropics (poleward of 20° latitude) SWOT will improve the resolution from currently about 100 km to a median of 51 or 74 km, depending on whether or not submesoscale balanced flows are energetic. Internal waves, in contrast to balanced flow, give rise to SSH variance spectra that drop off relatively gently with wavenumber, so SSH variance should become strongly dominated by internal waves in the submesoscale range. In situ observations of the internal-wave field suggest that the internal-wave signal accessible by SWOT will be largely dominated by internal tides. The internal-wave continuum is estimated to have a spectral level close to but somewhat lower than SWOT’s expected noise level.

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Jörn Callies and Raffaele Ferrari

Abstract

Submesoscale (1–200 km) wavenumber spectra of kinetic and potential energy and tracer variance are obtained from in situ observations in the Gulf Stream region and in the eastern subtropical North Pacific. In the Gulf Stream region, steep kinetic energy spectra at scales between 200 and 20 km are consistent with predictions of interior quasigeostrophic–turbulence theory, both in the mixed layer and in the thermocline. At scales below 20 km, the spectra flatten out, consistent with a growing contribution of internal-wave energy at small scales. In the subtropical North Pacific, the energy spectra are flatter and inconsistent with predictions of interior quasigeostrophic–turbulence theory. The observed spectra and their dependence on depth are also inconsistent with predictions of surface quasigeostrophic–turbulence theory for the observed ocean stratification. It appears that unbalanced motions, most likely internal tides at large scales and the internal-wave continuum at small scales, dominate the energy spectrum throughout the submesoscale range. Spectra of temperature variance along density surfaces, which are not affected by internal tides, are also inconsistent with predictions of geostrophic-turbulence theories. Reasons for this inconsistency could be the injection of energy in the submesoscale range by small-scale baroclinic instabilities or modifications of the spectra by coupling between surface and interior dynamics or by ageostrophic frontal effects.

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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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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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Xiaozhou Ruan and Jörn Callies

Abstract

To close the abyssal overturning circulation, dense bottom water has to become lighter by mixing with lighter water above. This diapycnal mixing is strongly enhanced over rough topography in abyssal mixing layers, which span the bottom few hundred meters of the water column. In particular, mixing rates are enhanced over mid-ocean ridge systems, which extend for thousands of kilometers in the global ocean and are thought to be key contributors to the required abyssal water mass transformation. To examine how stratification and thus diabatic transformation is maintained in such abyssal mixing layers, this study explores the circulation driven by bottom-intensified mixing over mid-ocean ridge flanks and within ridge-flank canyons. Idealized numerical experiments show that stratification over the ridge flanks is maintained by submesoscale baroclinic eddies and that stratification within ridge-flank canyons is maintained by mixing-driven mean flows. These restratification processes affect how strong a diabatic buoyancy flux into the abyss can be maintained, and they are essential for maintaining the dipole in water mass transformation that has emerged as the hallmark of a diabatic circulation driven by bottom-intensified mixing.

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Jörn Callies, Oliver Bühler, and Raffaele Ferrari

Abstract

Spectral analysis is applied to infer the dynamics of mesoscale winds from aircraft observations in the upper troposphere and lower stratosphere. Two datasets are analyzed: one collected aboard commercial aircraft and one collected using a dedicated research aircraft. A recently developed wave–vortex decomposition is used to test the observations’ consistency with linear inertia–gravity wave dynamics. The decomposition method is shown to be robust in the vicinity of the tropopause if flight tracks vary sufficiently in altitude. For the lower stratosphere, the decompositions of both datasets confirm a recent result that mesoscale winds are consistent with the polarization and dispersion relations of inertia–gravity waves. For the upper troposphere, however, the two datasets disagree: only the research aircraft data indicate consistency with linear wave dynamics at mesoscales. The source of the inconsistency is a difference in mesoscale variance of the measured along-track wind component. To further test the observed flow’s consistency with linear wave dynamics, the ratio between tropospheric and stratospheric mesoscale energy levels is compared to a simple model of upward-propagating waves that are partially reflected at the tropopause. For both datasets, the observed energy ratio is roughly consistent with the simple wave model, but wave frequencies diagnosed from the data draw into question the applicability of the monochromatic theory at wavelengths smaller than 10 km.

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Jörn Callies, Roy Barkan, and Alberto Naveira Garabato

Abstract

While the distribution of kinetic energy across spatial scales in the submesoscale range (1–100 km) has been estimated from observations, the associated time scales are largely unconstrained. These time scales can provide important insight into the dynamics of submesoscale turbulence because they help quantify to what degree the flow is subinertial and thus constrained by Earth’s rotation. Here a mooring array is used to estimate these time scales in the northeast Atlantic. Frequency-resolved structure functions indicate that energetic wintertime submesoscale turbulence at spatial scales around 10 km evolves on time scales of about 1 day. While these time scales are comparable to the inertial period, the observed flow also displays characteristics of subinertial flow that is geostrophically balanced to leading order. An approximate Helmholtz decomposition shows the order 10-km flow to be dominated by its rotational component, and the root-mean-square Rossby number at these scales is estimated to be 0.3. This rotational dominance and Rossby numbers below one persist down to 2.6 km, the smallest spatial scale accessible by the mooring array, despite substantially superinertial Eulerian evolution. This indicates that the Lagrangian evolution of submesoscale turbulence is slower than the Eulerian time scale estimated from the moorings. The observations therefore suggest that, on average, submesoscale turbulence largely follows subinertial dynamics in the 1–100-km range, even if Doppler shifting produces superinertial Eulerian evolution. Ageostrophic motions become increasingly important for the evolution of submesoscale turbulence as the scale is reduced—the root-mean-square Rossby number reaches 0.5 at a spatial scale of 2.6 km.

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Henri F. Drake, Raffaele Ferrari, and Jörn Callies

Abstract

The emerging view of the abyssal circulation is that it is associated with bottom-enhanced mixing, which results in downwelling in the stratified ocean interior and upwelling in a bottom boundary layer along the insulating and sloping seafloor. In the limit of slowly varying vertical stratification and topography, however, boundary layer theory predicts that these upslope and downslope flows largely compensate, such that net water mass transformations along the slope are vanishingly small. Using a planetary geostrophic circulation model that resolves both the boundary layer dynamics and the large-scale overturning in an idealized basin with bottom-enhanced mixing along a midocean ridge, we show that vertical variations in stratification become sufficiently large at equilibrium to reduce the degree of compensation along the midocean ridge flanks. The resulting large net transformations are similar to estimates for the abyssal ocean and span the vertical extent of the ridge. These results suggest that boundary flows generated by mixing play a crucial role in setting the global ocean stratification and overturning circulation, requiring a revision of abyssal ocean theories.

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