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Gualtiero Badin and Richard G. Williams

Abstract

The effect of buoyancy forcing on the residual circulation in the Southern Ocean is examined in two different ways. First, the rates of water-mass transformation and formation are estimated using air–sea fluxes of heat and freshwater in the isopycnal framework developed by Walin, which is applied to two different air–sea flux climatologies and a reanalysis dataset. In the limit of no diabatic mixing and at a steady state, these air–sea flux estimates of water-mass transformation and formation are equivalent to estimating the residual circulation and the subduction rates in the upper ocean, respectively. All three datasets reveal a transformation of dense to light waters between σ = 26.8 and 27.2, as well as positive formation rates peaking at σ = 26.6, versus negative rates peaking at σ = 27. The transformation is achieved either by surface heating or freshwater inputs, although the magnitude of the formation rates varies in each case. Second, an idealized model of a mixed layer and adiabatic thermocline for a channel is used to illustrate how changes in ocean dynamics in the mixed layer and freshwater fluxes can modify the buoyancy fluxes and, thus, alter the residual circulation. Increasing the Ekman advection of cold water northward enhances the air–sea temperature difference and the surface heat flux into the ocean, which then increases the residual circulation; an increase in wind stress of 0.05 N m−2 typically increases the surface heat flux by 8 W m−2 and alters the peaks in formation rate by up to 8 Sv (1 Sv ≡ 106 m3 s−1). Conversely, increasing the eddy advection and diffusion leads to an opposing weaker effect; an increase in the eddy transfer coefficient of 500 m2 s−1 decreases the surface heat flux by 3 W m−2 and alters the peaks in formation rate by 1 Sv.

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Gualtiero Badin and Daniela I.V. Domeisen

Abstract

Southern Hemisphere (SH) stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products. The results are compared with the same analysis applied to the Northern Hemisphere (NH). The probability density functions (PDFs) for the SH show persistent deviations from a Gaussian distribution. The variability is given by white spectra for low frequencies, a slope of −1 for intermediate frequencies, and −3 slopes for high frequencies. Considering the time series for winter and summer separately, PDFs show a Gaussian distribution and the variability spectra change their slopes, indicating the role of the transition between winter and summer variability in shaping the time series. The correlation (D 2) and the Kaplan–Yorke (D KY) dimensions are estimated. A finite value of the dimensions can be computed for each variable and data product, except for the NCEP zonal-mean zonal wind and temperature data, which violate the requirement D 2D KY, possibly owing to the presence of spurious trends and inconsistencies in the data. The value of D 2 ranges between 2.6 and 3.9, while D KY ranges between 3.0 and 4.5. The results show that both D 2 and D KY display large variability in their values both for different datasets and for different variables within the same dataset. The variability of the values of D 2 and D KY thus leaves open the question about the existence of a low-dimensional attractor or if the finite dimensions of the system are the result of the projection of a larger attractor in a low-dimensional embedding space.

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Daniel Mukiibi, Gualtiero Badin, and Nuno Serra

Abstract

Three-dimensional (3D) finite-time Lyapunov exponents (FTLEs) are computed from numerical simulations of a freely evolving mixed layer (ML) front in a zonal channel undergoing baroclinic instability. The 3D FTLEs show a complex structure, with features that are less defined than the two-dimensional (2D) FTLEs, suggesting that stirring is not confined to the edges of vortices and along filaments and posing significant consequences on mixing. The magnitude of the FTLEs is observed to be strongly determined by the vertical shear. A scaling law relating the local FTLEs and the nonlocal density contrast used to initialize the ML front is derived assuming thermal wind balance. The scaling law only converges to the values found from the simulations within the pycnocline, while it displays differences within the ML, where the instabilities show a large ageostrophic component. The probability distribution functions of 2D and 3D FTLEs are found to be non-Gaussian at all depths. In the ML, the FTLEs wavenumber spectra display −1 slopes, while in the pycnocline, the FTLEs wavenumber spectra display −2 slopes, corresponding to frontal dynamics. Close to the surface, the geodesic Lagrangian coherent structures (LCSs) reveal a complex stirring structure, with elliptic structures detaching from the frontal region. In the pycnocline, LCSs are able to detect filamentary structures that are not captured by the Eulerian fields.

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Gualtiero Badin and Daniela I. V. Domeisen

Abstract

Northern Hemisphere stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products and two numerical model runs with different forcing. The time series show red spectra at all frequencies and the probability distribution functions show persistent deviations from a Gaussian distribution. An exception is given by the numerical model forced with perpetual winter conditions—a case that shows more variability and follows a Gaussian distribution, suggesting that the deviation from Gaussianity found in the observations is due to the transition between summer and winter variability. To search for the presence of a chaotic attractor the correlation dimension and entropy, the Lyapunov spectrum, and the associated Kaplan–Yorke dimension are estimated. A finite value of the dimensions can be computed for each variable and data product, with the correlation dimension ranging between 3.0 and 4.0 and the Kaplan–Yorke dimension between 3.3 and 5.5. The correlation entropy varies between 0.6 and 1.1. The model runs show similar values for the correlation and Lyapunov dimensions for both the seasonally forced run and the perpetual-winter run, suggesting that the structure of a possible chaotic attractor is not determined by the seasonality in the forcing, but must be given by other mechanisms.

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Gualtiero Badin, Amit Tandon, and Amala Mahadevan

Abstract

Using a process study model, the effect of mixed layer submesoscale instabilities on the lateral mixing of passive tracers in the pycnocline is explored. Mixed layer eddies that are generated from the baroclinic instability of a front within the mixed layer are found to penetrate into the pycnocline leading to an eddying flow field that acts to mix properties laterally along isopycnal surfaces. The mixing of passive tracers released on such isopycnal surfaces is quantified by estimating the variance of the tracer distribution over time. The evolution of the tracer variance reveals that the flow undergoes three different turbulent regimes. The first regime, lasting about 3–4 days (about 5 inertial periods) exhibits near-diffusive behavior; dispersion of the tracer grows nearly linearly with time. In the second regime, which lasts for about 10 days (about 14 inertial periods), tracer dispersion exhibits exponential growth because of the integrated action of high strain rates created by the instabilities. In the third regime, tracer dispersion follows Richardson’s power law. The Nakamura effective diffusivity is used to study the role of individual dynamical filaments in lateral mixing. The filaments, which carry a high concentration of tracer, are characterized by the coincidence of large horizontal strain rate with large vertical vorticity. Within filaments, tracer is sheared without being dispersed, and consequently the effective diffusivity is small in filaments. While the filament centers act as barriers to transport, eddy fluxes are enhanced at the filament edges where gradients are large.

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Gualtiero Badin, Richard G. Williams, Zhao Jing, and Lixin Wu

Abstract

Transformation and formation rates of water masses in the Southern Ocean are estimated in a neutral-surface framework using air–sea fluxes of heat and freshwater together with in situ estimates of diapycnal mixing. The air–sea fluxes are taken from two different climatologies and a reanalysis dataset, while the diapycnal mixing is estimated from a mixing parameterization applied to five years of Argo float data. Air–sea fluxes lead to a large transformation directed toward lighter waters, typically from −45 to −63 Sv (1 Sv ≡ 106 m3 s−1) centered at γ = 27.2, while interior diapycnal mixing leads to two weaker peaks in transformation, directed toward denser waters, 8 Sv centered at γ = 27.8, and directed toward lighter waters, −16 Sv centered at γ = 28.3. Hence, air–sea fluxes and interior diapycnal mixing are important in transforming different water masses within the Southern Ocean. The transformation of dense to lighter waters by diapycnal mixing within the Southern Ocean is slightly larger, though comparable in magnitude, to the transformation of lighter to dense waters by air–sea fluxes in the North Atlantic. However, there are significant uncertainties in the authors' estimates with errors of at least ±5 W m−2 in air–sea fluxes, a factor 4 uncertainty in diapycnal mixing and limited coverage of air–sea fluxes in the high latitudes and Argo data in the Pacific. These water mass transformations partly relate to the circulation in density space: air–sea fluxes provide a general lightening along the core of the Antarctic Circumpolar Current and diapycnal diffusivity is enhanced at middepths along the current.

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Daniela I. V. Domeisen, Gualtiero Badin, and Inga M. Koszalka

ABSTRACT

The North Atlantic Oscillation (NAO) and the Arctic Oscillation (AO) describe the dominant part of the variability in the Northern Hemisphere extratropical troposphere. Because of the strong connection of these patterns with surface climate, recent years have shown an increased interest and an increasing skill in forecasting them. However, it is unclear what the intrinsic limits of short-term predictability for the NAO and AO patterns are. This study compares the variability and predictability of both patterns, using a range of data and index computation methods for the daily NAO and AO indices. Small deviations from Gaussianity are found along with characteristic decorrelation time scales of around one week. In the analysis of the Lyapunov spectrum it is found that predictability is not significantly different between the AO and NAO or between reanalysis products. Differences exist, however, between the indices based on EOF analysis, which exhibit predictability time scales around 12–16 days, and the station-based indices, exhibiting a longer predictability of 18–20 days. Both of these time scales indicate predictability beyond that currently obtained in ensemble prediction models for short-term predictability. Additional longer-term predictability for these patterns may be gained through local feedbacks and remote forcing mechanisms for particular atmospheric conditions.

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Andrey Y. Shcherbina, Miles A. Sundermeyer, Eric Kunze, Eric D’Asaro, Gualtiero Badin, Daniel Birch, Anne-Marie E. G. Brunner-Suzuki, Jörn Callies, Brandy T. Kuebel Cervantes, Mariona Claret, Brian Concannon, Jeffrey Early, Raffaele Ferrari, Louis Goodman, Ramsey R. Harcourt, Jody M. Klymak, Craig M. Lee, M.-Pascale Lelong, Murray D. Levine, Ren-Chieh Lien, Amala Mahadevan, James C. McWilliams, M. Jeroen Molemaker, Sonaljit Mukherjee, Jonathan D. Nash, Tamay Özgökmen, Stephen D. Pierce, Sanjiv Ramachandran, Roger M. Samelson, Thomas B. Sanford, R. Kipp Shearman, Eric D. Skyllingstad, K. Shafer Smith, Amit Tandon, John R. Taylor, Eugene A. Terray, Leif N. Thomas, and James R. Ledwell

Abstract

Lateral stirring is a basic oceanographic phenomenon affecting the distribution of physical, chemical, and biological fields. Eddy stirring at scales on the order of 100 km (the mesoscale) is fairly well understood and explicitly represented in modern eddy-resolving numerical models of global ocean circulation. The same cannot be said for smaller-scale stirring processes. Here, the authors describe a major oceanographic field experiment aimed at observing and understanding the processes responsible for stirring at scales of 0.1–10 km. Stirring processes of varying intensity were studied in the Sargasso Sea eddy field approximately 250 km southeast of Cape Hatteras. Lateral variability of water-mass properties, the distribution of microscale turbulence, and the evolution of several patches of inert dye were studied with an array of shipboard, autonomous, and airborne instruments. Observations were made at two sites, characterized by weak and moderate background mesoscale straining, to contrast different regimes of lateral stirring. Analyses to date suggest that, in both cases, the lateral dispersion of natural and deliberately released tracers was O(1) m2 s–1 as found elsewhere, which is faster than might be expected from traditional shear dispersion by persistent mesoscale flow and linear internal waves. These findings point to the possible importance of kilometer-scale stirring by submesoscale eddies and nonlinear internal-wave processes or the need to modify the traditional shear-dispersion paradigm to include higher-order effects. A unique aspect of the Scalable Lateral Mixing and Coherent Turbulence (LatMix) field experiment is the combination of direct measurements of dye dispersion with the concurrent multiscale hydrographic and turbulence observations, enabling evaluation of the underlying mechanisms responsible for the observed dispersion at a new level.

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