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James C. McWilliams

Abstract

Observations of float trajectories and vertical density profiles from the Mid-Ocean Dynamics Experiment are analyzed in terms of a likely equation of motion for mesoscale eddies involving the conservation of quasi-geostrophic potential vorticity along horizontal particle paths. From maps of the potential vorticity a careful scale analysis is made to estimate both local values for the Rossby number and the relative dynamical contributions of the planetary vorticity gradient, the relative vorticity and the stretching of vortex lines in the vertical. The proposed conservation is verified, to within estimates of the likely error, at several depths where this error is sufficiently small. Furthermore, two regimes in time are found, one in which the dynamical balances are highly nonlinear and another, for longer time scales, in which they are marginally linear.

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James C. McWilliams

Abstract

From measurements made during the 1973 Mid-Ocean Dynamics Experiment in the western North Atlantic, horizontal maps of the total dynamic pressure (or, in the geostrophic approximation, streamfunction) have been constructed for different vertical levels and time periods by the interpolation technique of objective analysis. The space and time sampling of the observations—several tens of kilometers horizontally, hundreds of meters vertically and several days in time—were adequate for resolving mesoscale eddies. The data consisted of velocities (displacement rates) at 1500 m depth from neutrally buoyant floats and vertical density profiles throughout the water column. The resulting maps have been considered from several, essentially phenomenological, points of view. These include descriptions of the synoptic eddy structure, the time evolution and propagation of the eddies, the adequacy of linear modal vertical structure, and the correspondences and energy partition between motions in the two vertical modes.

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James C. Mcwilliams

Abstract

The quasi-geostrophic, small-amplitude free modes of oscillation are examined for a midlatitude ocean basin with mean currents. Attention is restricted to a particular class of mean currents which are solutions of nonlinear, inviscid and unforced equations and whose free modes are all stable ones. Among the free modes are ones confined to the narrow regions where the mean jets are strongest. These modes, dubbed “jet modes”, have the following properties: 1) their phase speed is in the direction of and of the order of magnitude of the mean jet maximum velocity; 2) they are vertically in phase and upper-layer intensified when the mean jet is upper-layer intensified in phase and the thermocline is shallow; 3) they have a broader horizontal scale in the deep water than in the thermocline; 4) they have horizontal critical layers whose local balance is a nonlinear rather than a frictional one; 5) their Doppler-shifted frequencies are proportional to a mean potential vorticity gradient dominated by the horizontal curvature of the, mean jet; 6) and their mean energy and potential vorticity flux divergences are small or—in the particular geometry of a channel—zero. It is argued that many of these features should characterize the transience of narrow jets in general, especially those features relating to the spatial structure of the modes. (The stability and dispersion relation characteristics should be more peculiar to the type of jet present.)

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James C. McWilliams

Abstract

The problem of geostrophic adjustment, originally considered by C.G. Rossby, is solved in an axisymmetric geometry for a continuously stratified fluid, where the adjusted final state is in hydrostatic, gradient-wind balance. This problem is relevant to the generation of submesoscale coherent vortices in the ocean: diapycnal mixing events can create a local anomaly of less strongly stratified fluid, which then develops a balancing circulation through adjustment. An analytical solution is obtained for a few uniform-density layers, and this is compared with numerical solutions for continuous stratification. In both representations, two-dimensional solutions are compared with axisymmetric ones.

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James C. McWilliams

Abstract

No abstract available.

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Rémi Tailleux and James C. McWilliams

Abstract

In layered models of the ocean, the assumption of a deep resting layer is often made, motivated by the surface intensification of many phenomena. The propagation speed of first-mode, baroclinic Rossby waves in such models is always faster than in models with all the layers active. The assumption of a deep-resting layer is not crucial for the phase-speed enhancement since the same result holds if the bottom pressure fluctuations are uncorrelated from the overlying wave dynamics.

In this paper the authors explore the relevance of this behavior to recent observational estimates of “too-fast” waves by Chelton and Schlax. The available evidence supporting this scenario is reviewed and a method that extends the idea to a continuously stratified fluid is developed. It is established that the resulting amplification factor is at leading order captured by the formula,
i1520-0485-31-6-1461-eq1
where C fast is the enhanced phase speed, C standard the standard phase speed, Φ1(z) is the standard first mode for the velocity and pressure, and H 0 is the reference depth serving to define it. In the case WKB theory is applicable in the vertical direction, the above formula reduces to
i1520-0485-31-6-1461-eq2
where Nb is the deep Brunt–Väisälä frequency and N its vertical average.

The amplification factor is computed from a global hydrographic climatology. The comparison with observational estimates shows a reasonable degree of consistency, although with appreciable scatter. The theory appears to do as well as the previously published mean-flow theories of Killworth et al. and others. The link between the faster mode and the surface-intensified modes occurring over steep topography previously discussed in the literature is also established.

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Sonya Legg and James C. McWilliams

Abstract

In regions of active oceanic convection, such as the Labrador Sea, small- and mesoscale spatial variability is observed in the temperature and salinity fields (T and S). Often T and S structures are “density-compensated,” with the density contribution of the S anomaly nearly equal and opposite to the contribution from the T anomaly;this is manifest as variability in the “spice” field, τ = αT + βS, where α and −β are the local expansion coefficients for T and S. Here the mechanisms for generating T and S variability by convection around a preexisting mesoscale eddy, with particular attention to τ variability, are investigated. The authors perform several numerical experiments with identical density stratification, mesoscale circulation, and surface buoyancy forcing, but with different combinations of T and S in the stratification and surface flux. In all cases with both T and S variations present, it is found that spice variability exceeds that of density. In particular, there are substantial heat and salt fluxes at the base of the convecting region where the density flux vanishes. This τ variability is well predicted by a simple parcel exchange scaling argument, and it depends on preexisting vertical and lateral τ gradients as well as the τ component of the surface forcing. The τ variance is generated both by upright plume convection and by slantwise mixing and lateral stirring associated with the convectively induced baroclinic instability of the mesoscale eddy. In regions dominated by convective plumes, τ variance is dissipated more rapidly than in regions where the fluxes primarily take the form of mesoscale interleaving.

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R. Saravanan and James C. McWilliams

Abstract

Ocean–atmosphere interaction plays a key role in climate fluctuations on interdecadal timescales. In this study, different aspects of this interaction are investigated using an idealized ocean–atmosphere model, and a hierarchy of uncoupled and stochastic models derived from it. The atmospheric component is an eddy-resolving two-level global primitive equation model with simplified physical parameterizations. The oceanic component is a zonally averaged sector model of the thermohaline circulation. The coupled model exhibits spontaneous oscillations of the thermohaline circulation on interdecadal timescales. The interdecadal oscillation has qualitatively realistic features, such as dipolar sea surface temperature anomalies in the extratropics. Atmospheric forcing of the ocean plays a dominant role in exciting this oscillation. Although the coupled model is in itself deterministic, it is convenient to conceptualize the atmospheric forcing arising from weather excitation as having stochastic time dependence. Spatial correlations inherent in the atmospheric low-frequency variability play a crucial role in determining the oceanic interdecadal variability, through a form of spatial resonance. Local feedback from the ocean affects the amplitude of the interdecadal variability. The spatial patterns of correlations between the atmospheric flow and the oceanic variability fall into two categories: (i) upstream forcing patterns, and (ii) downstream response patterns. Both categories of patterns are expressible as linear combinations of the dominant modes of variability associated with the uncoupled atmosphere.

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Sonya Legg and James C. McWilliams

Abstract

During the recent Labrador Sea Deep Convection Experiment, numerous isobaric floats were deployed. Interpretation of the quasi-Lagrangian measurements from these floats requires an understanding of any biases that may be introduced by the response of the floats to the flow in which they are embedded. To investigate the float measurement biases in convecting flow numerical simulations of isobaric floats in a domain containing several mesoscale eddies have been performed. When a surface heat loss is applied, spatially variable convective mixing and baroclinic instability result. The authors find that without surface cooling, probability density functions of Eulerian and isobaric float measurements of tracers and velocities are very similar, given an initial distribution of isobaric floats that is random with respect to the initial features of the tracer field. However, with cooling isobaric statistics are biased compared to the Eulerian statistics. In particular, in near-surface regions isobaric floats appear to oversample regions of dense downwelling fluid. Since in near-surface layers downwelling dense fluid is associated with convergence, a probable explanation of the isobaric float biases is a tendency for floats to concentrate in regions of horizontal convergence. Also, with cooling floats may be more easily exchanged between eddies and the ambient fluid. The escape of a float from an eddy can be identified from changes in the values of material tracers. The authors identify a positive skewness in the time derivative of the buoyancy measured by the individual near-surface floats as a indicator of convection in the presence of mesoscale eddies.

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Sonya Legg and James C. McWilliams

Abstract

Ocean convection often occurs in regions of mesoscale eddy activity, where convective mixing and geostrophic eddy dynamics interact. The authors examine the interactions between a group of geostrophic eddies and convective mixing induced by surface buoyancy loss through a series of numerical simulations using a nonhydrostatic Boussinesq model. The eddies are initially baroclinic, with a surface-intensified density anomaly and sheared flow, but they are stable to baroclinic instability because of their small size. In the absence of buoyancy loss, eddy mergers occur much as in previous studies of geostrophic turbulence. With the addition of surface buoyancy loss, the surface stratification is eroded by small-scale convection. The convective mixing is highly heterogeneous, being deeper in regions of weaker initial stratification and shallower in more strongly stratified regions. The deformation radius is reduced in mixing regions and the weakly stratified eddies become baroclinically unstable. The barotropic component of kinetic energy increases as convection proceeds, largely due to the conversion of the available potential energy of the eddies in the baroclinic instability process. The convective forcing therefore provides a means of increasing the barotropic component of the eddy kinetic energy, by enabling the baroclinic instability. The fluid is efficiently homogenized by the energetic eddy field, leading to a few isolated eddies separated by a well-mixed fluid. These simulations provide a possible explanation for energetic eddy fields observed during convective periods in the Labrador Sea.

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