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  • Author or Editor: J. H. LaCasce x
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J. H. LaCasce

Abstract

The properties of forced baroclinic, quasigeostrophic Rossby waves in an ocean basin are discussed, with emphasis on the apparent phase speed. The response to a traveling wave wind stress curl consists of three parts, two of which propagate westward and one that tracks the wind. The apparent phase speed in the basin interior depends on the relative sizes of the amplitudes of these three terms, which vary with forcing frequency and scale and with the size of the deformation radius. With low-frequency, large-scale forcing, one westward wave dominates and its phase speed is the long baroclinic Rossby wave speed. With smaller forcing scales, the component that tracks the wind is comparably strong, and the superposition with the dominant westward wave can produce augmented apparent phase speeds. At frequencies larger than the maximum free wave frequency (proportional to the deformation radius), the westward waves are trapped in deformation-scale boundary layers, yielding a weak, directly forced interior. The choice of boundary conditions is found to affect strongly the response. In contrast to wind forcing, forcing by an imposed boundary oscillation yields propagation at the long-wave speed over a wide range of forcing frequencies.

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J. H. LaCasce
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J. H. LaCasce

Abstract

The author derives baroclinic modes and surface quasigeostrophic (SQG) solutions with exponential stratification and compares the results to those obtained with constant stratification. The SQG solutions with exponential stratification decay more rapidly in the vertical and have weaker near-surface velocities. This then compounds the previously noted problem that SQG underpredicts the velocities associated with a given surface density anomaly.

The author also examines how the SQG solutions project onto the baroclinic modes. With constant stratification, SQG waves larger than deformation scale project primarily onto the barotropic mode and to a lesser degree onto the first baroclinic mode. However, with exponential stratification, the largest projection is on the first baroclinic mode. The effect is even more pronounced over rough bottom topography. Therefore, large-scale SQG waves will look like the first baroclinic mode and vice versa, with realistic stratification.

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J. H. LaCasce

Abstract

Velocity probability density functions (PDFs) are calculated using data from subsurface current meters in the western North Atlantic Ocean. The PDFs are weakly, but significantly, non-Gaussian. They deviate from normality because of an excess of energetic events, and there are evidently more such events in the main thermocline than in the deep ocean. The PDFs are also compared with those obtained from subsurface floats in the same region. The PDFs are statistically indistinguishable so long as the float data are averaged in appropriately sized bins. Taking too-small bins yields overly Gaussian float PDFs, and taking too-large bins yields too-non-Gaussian PDFs. With this caveat, the Lagrangian and Eulerian PDFs agree, consistent with expectations from theory and previous numerical simulations.

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J. H. LaCasce and J. Pedlosky

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 complete transit of the basin. For small Z, the instability is shown to be a triad instability; for large Z the instability is fundamentally similar to the Eady instability mechanism. For all Z, the growth rate is on the order of the vertical shear of the basic wave divided by the deformation radius. If the parametric dependence of Z on latitude is examined, the condition of unit Z separates latitudes south of which the Rossby wave may successfully cross the basin while north of which the wave will break down into small-scale eddies with a barotropic component. The boundary between the two corresponds to the domain boundary found in satellite measurements. Furthermore, the resulting barotropic wave field is shown to propagate at speeds about 2 times as large as the baroclinic speed, and this is offered as a consistent explanation of the observed discrepancy between the satellite observations of Chelton and Schlax and simple linear wave theory. Here it is suggested that Rossby basin modes, if they exist, would be limited to tropical domains and that a considerable part of the observed midlatitude eddy field north of that boundary is due to the instability of wind-forced, long Rossby waves.

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J. H. LaCasce and J. Wang

Abstract

A previously published method by Wang et al. for predicting subsurface velocities and density from sea surface buoyancy and surface height is extended by incorporating analytical solutions to make the vertical projection. One solution employs exponential stratification and the second has a weakly stratified surface layer, approximating a mixed layer. The results are evaluated using fields from a numerical simulation of the North Atlantic. The simple exponential solution yields realistic subsurface density and vorticity fields to nearly 1000 m in depth. Including a mixed layer improves the response in the mixed layer itself and at high latitudes where the mixed layer is deeper. It is in the mixed layer that the surface quasigeostrophic approximation is most applicable. Below that the first baroclinic mode dominates, and that mode is well approximated by the analytical solution with exponential stratification.

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J. H. LaCasce and Joseph Pedlosky

Abstract

The properties of baroclinic, quasigeostrophic Rossby basin waves are examined. Full analytical solutions are derived to elucidate the response in irregular basins, specifically in a (horizontally) tilted rectangular basin and in a circular one. When the basin is much larger than the (internal) deformation radius, the basin mode properties depend profoundly on whether one allows the streamfunction to oscillate at the boundary or not, as has been shown previously. With boundary oscillations, modes occur that have low frequencies and, with scale-selective dissipation, decay at a rate less than or equal to that of the imposed dissipation. These modes approximately satisfy the long-wave equation in the interior. Using both unforced and forced solutions, the variation of the response with basin geometry and dissipation is documented. The long-wave modes obtain with scale-selective dissipation, but also with damping that acts equally at all scales. One finds evidence of them as well in the forced response, even when the dissipation is weak and the corresponding free modes are apparently absent.

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J. H. LaCasce and Sjoerd Groeskamp

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The deformation radius is widely used as an indication of the eddy length scale at different latitudes. The radius is usually calculated assuming a flat ocean bottom. However, bathymetry alters the baroclinic modes and hence their deformation radii. In a linear quasigeostrophic two-layer model with realistic parameters, the deep flow for a 100-km wave approaches zero with a bottom ridge roughly 10 m high, leaving a baroclinic mode that is mostly surface trapped. This is in line with published current meter studies showing a primary EOF that is surface intensified and has nearly zero flow at the bottom. The deformation radius associated with this “surface mode” is significantly larger than that of the flat bottom baroclinic mode. Using World Ocean Atlas data, the surface radius is found to be 20%–50% larger over much of the globe, and 100% larger in some regions. This in turn alters the long Rossby wave speed, which is shown to be 1.5–2 times faster than over a flat bottom. In addition, the larger deformation radius is easier to resolve in ocean models.

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J. H. LaCasce and K. H. Brink

Abstract

The authors examine freely evolving geostrophic turbulence, in two layers over a linearly sloping bottom. The initial flow is surface trapped and subdeformation scale. In all cases with a slope, two components are found: a collection of surface vortices, and a bottom-intensified flow that has zero surface potential vorticity. The rate of spinup and the scale of the bottom flow depend on Λ ≡ F 2 U 1/β 2, which measures the importance of interfacial stretching to the bottom slope, with small values of Λ corresponding to a slow spinup and stronger along-isobath anisotropy. The slope also affects the mean size of the surface vortices, through the dispersal of flow at depth and by altering vortex stability. This too can be characterized in terms of the parameter, Λ.

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Francisco J. Beron-Vera and J. H. LaCasce

Abstract

Pair-separation statistics of in situ and synthetic surface drifters deployed near the Deepwater Horizon site in the Gulf of Mexico are investigated. The synthetic trajectories derive from a 1-km-resolution data-assimilative Navy Coastal Ocean Model (NCOM) simulation. The in situ drifters were launched in the Grand Lagrangian Deployment (GLAD). Diverse measures of the dispersion are calculated and compared to theoretical predictions. For the NCOM pairs, the measures indicate nonlocal pair dispersion (in which pair separations grow exponentially in time) at the smallest sampled scales. At separations exceeding 100 km, pair motion is uncorrelated, indicating absolute rather than relative dispersion. With the GLAD drifters, however, the statistics are ambiguous, with some indicating local dispersion (in which pair separations exhibit power-law growth) and others suggesting nonlocal dispersion. The difference between the two datasets stems in part from inertial oscillations, which affect the energy levels at small scales without greatly altering pair dispersion. These were significant in GLAD but much weaker in the NCOM simulation. In addition, the GLAD drifters were launched over a limited geographical area, producing few independent realizations and hence lower statistical significance. Restricting the NCOM set to pairs launched at the same locations yields very similar results, suggesting the model is for the most part capturing the observed dispersion.

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