Shane R. Keating

Diagnosing Lateral Mixing in the Upper Ocean with Virtual Tracers: Spatial and Temporal Resolution Dependence

Several recent studies diagnose lateral stirring and mixing in the upper ocean using altimetry-derived velocity fields to advect ‘‘virtual’’ particles and fields offline. However, the limited spatiotemporal resolution of altimetric maps leads to errors in the inferred diagnostics, because unresolved scales are necessarily imperfectly modeled. The authors examine a range of tracer diagnostics in two models of baroclinic turbulence: the standard Phillips model, in which dispersion is controlled by large-scale eddies, and the Eady model, where dispersion is determined by local scales of motion. These models serve as a useful best- and worst-case comparison and a valuable test of the resolution sensitivity of tracer diagnostics. The effect of unresolved scales is studied by advecting tracers using model velocity fields subsampled in space and time and comparing the derived tracer diagnostics with their ‘‘true’’ value obtained from the fully resolved flow. The authors find that eddy diffusivity and absolute dispersion, which are governed by largescaledynamics,areinsensitivetospatialsamplingerrorin eitherflow.Measuresthatdependstronglyonsmall scales, such as relative dispersion andfinite-timeLyapunov exponents, are highly sensitive to spatial sampling in the Eady model. Temporal sampling error is found to have a more complicated behavior because of the onset of particle overshoot leading to scrambling of Lagrangian diagnostics. This leads to a potential restrictionontheutilityofrawaltimetrymapsforstudyingmixingintheupperocean.Theauthorsconcludethat offline diagnostics of mixing in ocean flows with an energized submesoscale should be viewed with some caution.

New Methods for Estimating Ocean Eddy Heat Transport Using Satellite Altimetry

AbstractAttempts to monitor ocean eddy heat transport are strongly limited by the sparseness of available observations and the fact that heat transport is a quadratic, sign-indefinite quantity that is particularly sensitive to unresolved scales. In this article, a suite of stochastic filtering strategies for estimating eddy heat transport are tested in idealized two-layer simulations of mesoscale oceanic turbulence at high and low latitudes under a range of observation scenarios. A novel feature of these filtering strategies is the use of computationally inexpensive stochastic models to forecast the underlying nonlinear dynamics. The stochastic model parameters can be estimated by regression fitting to climatological energy spectra and correlation times or by adaptively learning these parameters “on-the-fly” from the observations themselves.The authors show that, by extracting high-wavenumber information that has been aliased into the low wavenumber band, “stochastically super-resolved” velocity fields wi...

Diagnosing Ocean Stirring: Comparison of Relative Dispersion and Finite-Time Lyapunov Exponents

AbstractThe relationship between two commonly used diagnostics of stirring in ocean and atmospheric flows, the finite-time Lyapunov exponents λ and relative dispersion R2, is examined for a simple uniform strain flow and ocean flow inferred from altimetry. Although both diagnostics are based on the separation of initially close particles, the two diagnostics measure different aspects of the flow and, in general, there is not a one-to-one relationship between the diagnostics. For a two-dimensional flow with time-independent uniform strain, there is a single time-independent λ, but there is a wide range of values of R2 for individual particle pairs. However, it is shown that the upper and lower limits of R2 for individual pairs, the mean value over a large ensemble of pairs, and the probability distribution function (PDF) of R2 have simple relationships with λ. Furthermore, these analytical expressions provide a reasonable approximation for the R2–λ relationship in the surface ocean flow based on geostrophi...

Homogenization and mixing measures for a replenishing passive scalar field

The efficiency with which an incompressible flow mixes a passive scalar field that is continuously replenished by a steady source-sink distribution has been quantified using the suppression of the mean scalar variance below the value it would attain in the absence of the stirring. We examine the relationship this mixing measure has to the effective diffusivity obtained from homogenization theory, particularly establishing precise connections in the case of a stirring velocity field that is periodic in space and time and varies on scales much smaller than that of the source. We explore theoretically and numerically via the Childress–Soward family of flows how the mixing measures lose their linkage to the homogenized diffusivity when the velocity and source field do not enjoy scale separation. Some implications for homogenization-based parametrizations of mixing by flows with finite scale separation are discussed.

Lagrangian and Eulerian characterization of two counter‐rotating submesoscale eddies in a western boundary current

In recent decades, high-spatial resolution ocean radar and satellite imagery measurements have revealed a complex tangle of submesoscale filaments and eddies, in the surface velocity, temperature, and chlorophyll a fields. We use a suite of high-resolution data to characterize two counter-rotating, short-lived eddies formed at the front between the warm East Australian Current (EAC) and temperate coastal waters (308S, Eastern Australia). In this region, submesoscale filaments and short-lived eddies are dynamically generated and decay at time scales of hours to days. Dominant cyclonic filaments of O(1) Rossby number formed along frontal jets and eddy boundaries, generating localized ageostrophic circulations at the submesoscale. Measurements of over-ocean wind direction and surface currents from high-frequency radars reveal the influence of the short-term, small-scale wind forcing on the surface circulation, enhancement of the horizontal shear, frontal jet destabilization, and the generation and decay of the cyclonic eddy. By contrast, the anticyclonic eddy formation was most likely associated with EAC mesoscale instability and anticyclonic vorticity. Lagrangian tracks show that surface particles can be temporarily trapped in the eddies and frontal convergent zones, limiting their transport. Mixing between EAC-derived and coastal waters was increased along the frontal regions, and particles starting at the divergent regions around the eddies experienced significant dispersion at submesoscales. The cyclonic cold-core eddy entrained high chlorophyll a shelf waters on its convergent side, suggesting spiral eddy cyclogenesis.

Pairwise surface drifter separation in the western Pacific sector of the Southern Ocean

The Southern Ocean plays a critical role in global climate, yet the mixing properties of the circulation in this part of the ocean remain poorly understood. Here dispersion in the vicinity of the Southern Antarctic Circumpolar Current Front, one of the branches of the Antarctic Circumpolar Current, is studied using 10 pairs of surface drifters deployed systematically across the frontal jet and its flanks. Drifter pairs were deployed with an initial separation of 13 m and report their position every hour. The separation of the pairs over 7 months, in terms of their Finite-Scale Lyapunov Exponents (FSLE), dispersion, and diffusivity, is characterized and related to expected behavior from Quasi-Geostrophic (QG) and Surface Quasi-Geostrophic (SQG) theories. The FSLE analysis reveals two submesoscale regimes, with SQG-like behavior at scales below 3.2 km and mixed QG/SQG behavior at scales between 3.2 and 73 km. The dispersion analysis, however, suggests QG-like behavior for the smallest scales. Both dispersion and diffusivity appear isotropic for scales up to 500 km. Finally, there is no clear indication of a cross-jet variation of drifter dispersion.

Turbulent resistivity in wavy two-dimensional magnetohydrodynamic turbulence

The theory of turbulent resistivity in ‘wavy’ magnetohydrodynamic turbulence in two dimensions is presented. The goal is to explore the theory of quenching of turbulent resistivity in a regime for which the mean field theory can be rigorously constructed at large magnetic Reynolds number Rm . This is achieved by extending the simple two-dimensional problem to include body forces, such as buoyancy or the Coriolis force, which convert large-scale eddies into weakly interacting dispersive waves. The turbulence-driven spatial flux of magnetic potential is calculated to fourth order in wave slope – the same order to which one usually works in wave kinetics. However, spatial transport, rather than spectral transfer, is the object here. Remarkably, adding an additional restoring force to the already tightly constrained system of high Rm magnetohydrodynamic turbulence in two dimensions can actually increase the turbulent resistivity, by admitting a spatial flux of magnetic potential which is not quenched at large Rm , although it is restricted by the conditions of applicability of weak turbulence theory. The absence of Rm -dependent quenching in this wave-interaction-driven flux is a consequence of the presence of irreversibility due to resonant nonlinear three-wave interactions, which are independent of collisional resistivity. The broader implications of this result for the theory of mean field electrodynamics are discussed.

Upper ocean flow statistics estimated from superresolved sea‐surface temperature images

Ocean turbulence on scales of 10–50 km plays a key role in biogeochemical processes, frontal dynamics, and tracer transport in the upper ocean, but our understanding of these scales is limited because they are too small to be resolved using extant satellite altimetry products. By contrast, microwave imagery of the sea-surface temperature field does resolve these scales and can be used to estimate the upper ocean flow field due to the strong correlation between the surface density field and the interior potential vorticity. However, because the surface density (or temperature) is a smoothed version of the geostrophic stream function, the resulting velocity field estimates are limited to scales of 100–300 km in the first few hundred meters of the water column. A method is proposed for generating superresolved sea-surface temperature images using direct low-resolution (microwave) temperature observations in combination with an empirical parameterization for the unresolved scales modeled on statistical information from high-resolution (infrared) imagery. Because the method relies only on the statistics of the small-scale field, it is insensitive to data outages due to cloud cover that affect infrared observations. The method enhances the effective resolution of the temperature images by exploiting the effect of spatial aliasing and generates an optimal estimate of the small-scale temperature field using standard Bayesian inference. The technique is tested in quasigeostrophic simulations driven by realistic climatological shear and stratification profiles for three contrasting regions at high, middle, and low latitudes. The resulting superresolved sea-surface temperature images are then used to estimate the three-dimensional velocity field in the upper ocean on scales of 10–50 km.

The Kinematic Similarity of Two Western Boundary Currents Revealed by Sustained High‐Resolution Observations

Western boundary currents (WBCs) modulate the global climate and dominate regional ocean dynamics. However, detailed inter-comparisons of the kinematic structure of WBCs have been hindered by a lack of sustained observational datasets. Here we compare multi-year, highresolution observations (1km, hourly) of surface currents in two WBCs (Florida Current and East Australian Current) upstream of their separation point. Current variability is dominated by meandering, and the WBCs exhibit contrasting time-mean velocities in an Eulerian coordinate frame. By transforming to a jet-following coordinate frame, we find that the timemean surface velocity structure of the WBC jets are remarkably similar, despite contrasting local wind, bathymetry, and meandering signal. Both WBCs show steep submesoscale kinetic energy wavenumber spectra with weak seasonal variability, in contrast to recent findings in other ocean regions. Our results suggest that it is the mesoscale flow field that controls mixing and ocean dynamics in these regions.

Jet–Topography Interactions Affect Energy Pathways to the Deep Southern Ocean

AbstractIn the Southern Ocean, strong eastward ocean jets interact with large topographic features, generating eddies that feed back onto the mean flow. Deep-reaching eddies interact with topography, where turbulent dissipation and generation of internal lee waves play an important role in the ocean’s energy budget. However, eddy effects in the deep ocean are difficult to observe and poorly characterized. This study investigates the energy contained in eddies at depth, when an ocean jet encounters topography. This study uses a two-layer ocean model in which an imposed unstable jet encounters a topographic obstacle (either a seamount or a meridional ridge) in a configuration relevant to an Antarctic Circumpolar Current frontal jet. The authors find that the presence of topography increases the eddy kinetic energy (EKE) at depth but that the dominant processes generating this deep EKE depend on the shape and height of the obstacle as well as on the baroclinicity of the jet before it encounters topography. I...