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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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Albion Lawrence
and
Jörn Callies

Abstract

Along-track wavenumber spectral densities of sea surface height (SSH) are estimated from Jason-2 altimetry data as a function of spatial location and calendar month to understand the seasonality of meso- and submesoscale balanced dynamics across the global ocean. Regions with significant mode-1 and mode-2 baroclinic tides are rejected, restricting the analysis to the extratropics. Where balanced motion dominates, the SSH spectral density is averaged over all pass segments in a region for each calendar month and is fit to a four-parameter model consisting of a flat plateau at low wavenumbers, a transition at wavenumber k 0 to a red power law spectrum k s , and a white spectrum at high wavenumbers that models the altimeter noise. The monthly time series of the model parameters are compared to the evolution of the mixed layer. The annual mode of the spectral slope s reaches a minimum after the mixed layer deepens, and the annual mode of the bandpassed kinetic energy in the ranges [2k 0, 4k 0] and [k 0, 2k 0] peak ∼2 and ∼4 months, respectively, after the maximum of the annual mode of the mixed layer depth. This analysis is consistent with an energization of the submesoscale by a winter mixed layer instability followed by an inverse cascade of kinetic energy to the mesoscale, in agreement with prior modeling studies and in situ measurements. These results are compared to prior modeling, in situ, and satellite investigations of specific regions and are broadly consistent with them within measurement uncertainties.

Significance Statement

This paper uses satellite observations to understand the source of ocean dynamics at the 1–100-km scales at which vertical motion becomes important and which are thus relevant for biology and for the exchange of heat and carbon with the atmosphere. The observations are consistent with a seasonal variation of dynamics at these scales, predicted by a specific theory of upper-ocean turbulence and confirmed by modeling studies and regional observations. We update prior satellite-based studies by excluding regions with competing effects, by our treatment of the noise, and by our characterization of the seasonality. This work provides a template for analyzing data from the upcoming Surface Water and Ocean Topography (SWOT) satellite.

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Yangcheng Luo
and
Jörn Callies

Abstract

Submesoscale turbulence in the upper ocean consists of fronts, filaments, and vortices that have horizontal scales on the order of 100 m to 10 km. High-resolution numerical simulations have suggested that submesoscale turbulence is associated with strong vertical motion that could substantially enhance the vertical exchange between the thermocline and mixed layer, which may have an impact on marine ecosystems and climate. Theoretical, numerical, and observational work indicates that submesoscale turbulence is energized primarily by baroclinic instability in the mixed layer, which is most vigorous in winter. This study demonstrates how such mixed layer baroclinic instabilities induce vertical exchange by drawing filaments of thermocline water into the mixed layer. A scaling law is proposed for the dependence of the exchange on environmental parameters. Linear stability analysis and nonlinear simulations indicate that the exchange, quantified by how much thermocline water is entrained into the mixed layer, is proportional to the mixed layer depth, is inversely proportional to the Richardson number of the thermocline, and increases with increasing Richardson number of the mixed layer. The results imply that the tracer exchange between the thermocline and mixed layer is more efficient when the mixed layer is thicker, when the mixed layer stratification is stronger, when the lateral buoyancy gradient is stronger, and when the thermocline stratification is weaker. The scaling suggests vigorous exchange between the permanent thermocline and deep mixed layers in winter, especially in mode water formation regions.

Significance Statement

This study examines how instabilities in the surface layer of the ocean bring interior water up from below. This interior–surface exchange can be important for dissolved gases such as carbon dioxide and oxygen as well as nutrients fueling biological growth in the surface ocean. A scaling law is proposed for the dependence of the exchange on environmental parameters. The results of this study imply that the exchange is particularly strong if the well-mixed surface layer is thick, lateral density gradients are strong (such as at fronts), and the stratification below the surface layer is weak. These theoretical findings can be implemented in boundary layer parameterization schemes in global ocean models and improve our understanding of the marine ecosystem and how the ocean mediates climate change.

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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

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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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
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
,
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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Henry G. Peterson
and
Jörn Callies

Abstract

To close the overturning circulation, dense bottom water must upwell via turbulent mixing. Recent studies have identified thin bottom boundary layers (BLs) as locations of intense upwelling, yet it remains unclear how they interact with and shape the large-scale circulation of the abyssal ocean. The current understanding of this BL–interior coupling is shaped by 1D theory, suggesting that variations in locally produced BL transport generate exchange with the interior and thus a global circulation. Until now, however, this picture has been based on a 1D theory that fails to capture the local evolution in even highly idealized 2D geometries. The present work applies BL theory to revised 1D dynamics, which more naturally generalizes to two and three dimensions. The BL is assumed to be in quasi-equilibrium between the upwelling of dense water and the convergence of downward buoyancy fluxes. The BL transport, for which explicit formulas are presented, exerts an influence on the interior by modifying the bottom boundary condition. In 1D, this BL transport is independent of the interior evolution, but in 2D the BL and interior are fully coupled. Once interior variables and the bottom slope are allowed to vary in the horizontal, the resulting convergences and divergences in the BL transport exchange mass with the interior. This framework allows for the analysis of previously inaccessible problems such as the BL–interior coupling in the presence of an exponential interior stratification, laying the foundation for developing a full theory for the abyssal circulation.

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