J. H. LaCasce

Relative dispersion at the surface of the Gulf of Mexico

We examine the relative motion of pairs and triplets of surface drifters in the Gulf of Mexico. The mean square pair separations grow exponentially in time from the smallest resolved scale (1 km) to 40‐ 50 km, with an e-folding time of 2‐ 3 days. Thereafter, the dispersion exhibits a power law dependence on time with an exponent of between 2 and 3 (depending on the measure used) up to scales of several hundred kilometers. The straining is for the most part isotropic, with only weak regional variations. But there are suggestions of anisotropy in the western basin, probably due to boundary current advection. The pair velocities are correlated during the early phase and a portion of the late phase. The relative displacement distributions during the early phase are, after an initial adjustment, nonGaussian and approximately constant, suggestive of local straining. The triplet results likewise suggest two growth phases. During the early phase, the mean area and the longest triangle leg grow exponentially in time, the latter with a rate consistent with the two-particle results. Most triangles are drawn out during this time. During the late period, the triangles grow and their aspect ratios systematically decrease, suggesting an evolution to an equilateral shape. Although surface divergences should affect these statistics, they nevertheless strongly resemble those found with two-dimensional turbulent e ows. If so, we would infer an enstrophy cascade at scales below the deformation radius (40‐ 50 km) which is probably spectrally local. The latter implies that growth in particle separations comes from e ow features the same size as the separations. It is also possible there is an inverse energy cascade to scales larger than the deformation radius, driven possibly by baroclinic instability. However, the late period statistics may also ree ect dispersion by a large scale shear.

Relative dispersion in the subsurface North Atlantic

Pair statistics are calculated for subsurface floats in the North Atlantic. The relative diffusivity (the derivative of the mean square particle separation) is approximately constant at large scales in both eastern and western basins, though the implied scale of the energy-containing eddies is greater in the west. But the behavior at times soon after pair deployment is quite different in the two basins; in the west the diffusivity grows approximately as distance to the 4/3 power, consistent with an inverse turbulent cascade of energy (or possibly of mixing superimposed on a mean shear), but in the east the diffusivity grows more slowly, as for instance in simple stochastic systems. Exponential stretching, expected in an enstrophy cascade, is not resolved in any region; however, this may reflect only that the present pair separations are too large initially.

Estimating subsurface horizontal and vertical velocities from sea-surface temperature

We examine a dynamical method for estimating subsurface fields (density, pressure, horizontal and vertical velocities) in the upper ocean using sea-surface temperature (SST) and a climatological estimate of the stratification. The method derives from the “surface quasi-geostrophic” (SQG) approximation. The SST is used to generate a potential vorticity (PV) field which is then inverted for the pressure. We examine first the standard SQG model, in which the PV is assumed trapped in a delta-function layer at the surface. We then modify the model by introducing a subsurface PV which is proportional to the surface density and decays exponentially with depth. We derive the subsurface density from the hydrostatic relation, the horizontal velocities from geostrophy and the subsurface vertical velocities from the quasi-geostrophic omega equation. We compare the predicted densities and velocities with those from a three-dimensional (3D) ocean model, and from in situ measurements in the Mediterranean, Eastern Pacific and the Azores Current. In most cases the standard SQG model predicts the qualitative structure of the subsurface flow. But it also underestimates its strength. The modified model yields better estimates of both the strength and vertical structure of the subsurface flow.

On the Obscurantist Physics of “Form Drag” in Theorizing about the Circumpolar Current

Abstract The authors point out that, since the “form-drag” force balance commonly advanced for the Antarctic Circumpolar Current is really just a statement that northward Ekman transport in the circumpolar Drake Passage zone is compensated by deep southward geostrophic flow, the balance is actually irrelevant to the magnitude of the current itself. It is thus misleading to ascribe a role to form drag in its physics. Sverdrup dynamics seems to offer a more promising analysis of the real Circumpolar Current–as proposed long ago.

The Instability of Rossby Basin Modes and the Oceanic Eddy Field

Abstract Low-frequency, large-scale baroclinic Rossby basin modes, resistant to scale-dependent dissipation, have been recently theoretically analyzed and discussed as possible efficient coupling agents with the atmosphere for interactions on decadal time scales. Such modes are also consistent with evidence of the westward phase propagation in satellite altimetry data. In both the theory and the observations, the scale of the waves is large in comparison with the Rossby radius of deformation and the orientation of fluid motion in the waves is predominantly meridional. These two facts suggest that the waves are vulnerable to baroclinic instability on the scale of the deformation radius. The key dynamical parameter is the ratio Z of the transit time of the long Rossby wave to the e-folding time of the instability. When this parameter is small the wave easily crosses the basin largely undisturbed by the instability; if Z is large the wave succumbs to the instability and is largely destroyed before making a c...

Velocity Probability Density Functions for Oceanic Floats

Probability density functions (PDFs) of daily velocities from subsurface floats deployed in the North Atlantic and equatorial Atlantic Oceans are examined. In general, the PDFs are approximately Gaussian for small velocities, but with significant exponential tails for large velocities. Correspondingly, the kurtoses of the distributions are greater than three. Similar PDFs are found in both western and eastern regions, above and below 1000-m depth, with more significant non-Gaussianity in the North Atlantic than at the equator. Analogously, Lagrangian statistics in decaying two-dimensional turbulence also display non-Gaussian velocity PDFs with approximately exponential tails, in the limit of large Reynolds number.

Wind-Driven Variability of the Large-Scale Recirculating Flow in the Nordic Seas and Arctic Ocean

The varying depth-integrated currents in the Nordic seas and Arctic Ocean are modeled using an integral equation derived from the shallow-water equations. This equation assumes that mass divergence in the surface Ekman layer is balanced by convergence in the bottom Ekman layer. The primary flow component follows contours of f /H. The model employs observed winds and realistic bottom topography and has one free parameter, the coefficient of the (linear) bottom drag. The data used for comparison are derived from in situ current meters, satellite altimetry, and a primitive equation model. The current-meter data come from a 4-yr record at 75 8 Ni n the Greenland Sea. The currents here are primarily barotropic, and the model does well at simulating the variability. The ‘‘best’’ bottom friction parameter corresponds to a spindown time of 30‐60 days. A further comparison with bottom currents from a mooring on the Norwegian continental slope, deployed over one winter period, also shows reasonable correspondence. The principal empirical orthogonal function obtained from satellite altimetry data in the Nordic seas has a spatial structure that closely resembles f /H. A direct comparison of this mode’s fluctuations with those predicted by the theoretical model yields linear correlation coefficients in the range 0.75‐0.85. The primitive equation model is a coupled ocean‐ice version of the Princeton Ocean Model for the North Atlantic and Arctic. Monthly mean depth-averaged velocities are calculated from a 42-yr integration and then compared with velocities predicted from an idealized model driven by the same reanalyzed atmospheric winds. In the largely ice-free Norwegian Sea, the coherences between the primitive equation and idealized model velocities are as high as 0.9 on timescales of a few months to a few years. They are lower in the remaining partially or fully ice-covered basins of the Greenland Sea and the Arctic Ocean, presumably because ice alters the momentum transferred to the ocean by the wind. The coherence in the Canadian Basin of the Arctic can be increased substantially by forcing the idealized model with ice velocities rather than the wind. Estimates of the depth-integrated vorticity budget in the primitive equation model suggest that bottom friction is important but that lateral diffusion is of equal or greater importance in compensating surface Ekman pumping.

Relative dispersion in the Nordic Seas

We examine the relative dispersion of surface drifters deployed in the POLEWARD experiment in the Nordic Seas during 2007–2008. The drifters were launched in pairs and triplets, yielding 67 pairs with an initial separation of 2 km or less. There were 26 additional pairs from drifters which subsequently came near one another. As these produced statistically identical dispersion to the original pairs, we used them as well, yielding 93 pairs. The relative dispersion exhibits three phases. The first occurs during the first two days, at spatial scales less than 10 km. The dispersion increases approximately exponentially during this period, with an e-folding time of roughly half a day. During the second phase, from 2 to roughly 10 days and scales of 10 to roughly 100 km, the dispersion increases as a power law, with r2 α t3. At the largest spatial and temporal scales, the dispersion increases linearly in time and the pair velocities are uncorrelated, consistent with diffusive spreading. We use a stochastic model with a representative mean flow to test the effect of the mean shear on dispersion. The model produces dispersion comparable to the observed during the second and third phases but fails to capture other statistics, such as the PDFs of the displacements. These statistics are instead suggestive of an inverse energy cascade, from the deformation scale up to 100 km.

Estimating suppression of eddy mixing by mean flows

Particle- and tracer-based estimates of lateral diffusivities are used to estimate the suppression of eddy mixingacrossstrongcurrents.Particlesandtracersare advectedusingavelocityfieldderivedfromseasurface height measurements from the South Pacific, in a region west of Drake Passage. This velocity field has been used in a companion paper to show that both particle- and tracer-based estimates of eddy diffusivities are equivalent, despite recent claims to the contrary. These estimates of eddy diffusivities are here analyzed to show 1) that the degree of suppression of mixing across the strong Antarctic Circumpolar Current is correctly predicted by mixing length theory modified to include eddy propagation along the mean flow and 2) that the suppressioncan beinferredfromparticletrajectoriesby studyingthestructureofthe autocorrelationfunction of the particle velocities beyond the first zero crossing. These results are then used to discuss how to compute lateral and vertical variations in eddy diffusivities using floats and drifters in the real ocean.

The velocity distribution of barotropic turbulence

We study the statistical properties of the velocity and velocity gradient distributions in barotropic turbulence. At large enough Reynolds number, the velocity distribution becomes non-Gaussian outside the vortex cores, and its characteristics are completely determined by the properties of the far field induced by the coherent vortices. The velocity gradients are always non-Gaussian inside coherent vortices, due to the spatial velocity correlations associated with the ordered flow in the vortex cores, and become non-Gaussian also in the background turbulence at large enough Reynolds number.