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Miles A. Sundermeyer and M-Pascale Lelong

Abstract

In this second of two companion papers, numerical simulations of lateral dispersion by small-scale geostrophic motions, or vortical modes, generated by the adjustment of mixed patches following diapycnal mixing events are examined. A three-dimensional model was used to solve the Navier–Stokes equations and an advection/diffusion equation for a passive tracer. Model results were compared with theoretical predictions for vortical mode stirring with results from dye release experiments conducted over the New England continental shelf. For “weakly nonlinear” cases in which adjustment events were isolated in space and time, lateral dispersion in the model was consistent to within a constant scale factor with the parameter dependence
i1520-0485-35-12-2368-eq1
predicted by Sundermeyer et al., where h and L are the vertical and horizontal scales of the mixed patches, ΔN2 is the change in stratification associated with the mixed patches, f is the Coriolis parameter, ϕ is the frequency of diapycnal mixing events, and νB is the background viscosity. The associated scale factor, assumed to be of order 1, had an actual value of about 7, although this value will depend, in an unknown way, on the assumed horizontal scale of the mixed patches, which was here held constant at close to the deformation radius. A second more energetic parameter regime was also identified in which vortical mode stirring became strongly nonlinear and the effective lateral dispersion was larger. Estimates of the relevant parameters over the New England shelf suggest that this strongly nonlinear regime is more relevant to the real ocean than the weakly nonlinear regime, at least under late summer conditions. This suggests that stirring by small-scale geostrophic motion may, under certain conditions, contribute significantly to lateral dispersion on scales of 1–10 km in the ocean.
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M-Pascale Lelong and Miles A. Sundermeyer

Abstract

In this first of two companion papers, the time-dependent relaxation of an isolated diapycnal mixing event is examined in detail by means of numerical simulations, with an emphasis on the energy budget, particle displacements, and their implications for submesoscale oceanic lateral dispersion. The adjustment and dispersion characteristics are examined as a function of the lateral extent of the event L relative to the Rossby radius of deformation R. The strongest circulations and horizontal displacements occur in the regime R/LO(1). For short times, less than an inertial period, horizontal displacements are radial. Once the adjustment is completed, displacements become primarily azimuthal and continue to stir fluid over several to tens of inertial periods. The cumulative effect of many such events in terms of the effective lateral dispersion that they induce is examined in the companion paper.

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I. I. Rypina, A. Kirincich, S. Lentz, and M. Sundermeyer

Abstract

This paper aims to test the validity, utility, and limitations of the lateral eddy diffusivity concept in a coastal environment through analyzing data from coupled drifter and dye releases within the footprint of a high-resolution (800 m) high-frequency radar south of Martha’s Vineyard, Massachusetts. Specifically, this study investigates how well a combination of radar-based velocities and drifter-derived diffusivities can reproduce observed dye spreading over an 8-h time interval. A drifter-based estimate of an anisotropic diffusivity tensor is used to parameterize small-scale motions that are unresolved and underresolved by the radar system. This leads to a significant improvement in the ability of the radar to reproduce the observed dye spreading.

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Anne-Marie E. G. Brunner-Suzuki, Miles A. Sundermeyer, and M.-Pascale Lelong

Abstract

The effect of a large-scale internal wave on a multipolar compound vortex was simulated numerically using a 3D Boussinesq pseudospectral model. A suite of simulations tested the effect of a background internal wave of various strengths, including a simulation with only a vortex. Without the background wave, the vortex remained apparently stable for many hundreds of inertial periods but then split into two dipoles. With increasing background wave amplitude, and hence shear, dipole splitting occurred earlier and was less symmetric in space. Theoretical considerations suggest that the vortex alone undergoes a self-induced mixed barotropic–baroclinic instability. For a vortex plus background wave, kinetic energy spectra showed that the internal wave supplied energy for the dipole splitting. In this case, it was found that the presence of the wave hastened the time to instability by increasing the initial perturbation to the vortex. Results suggest that the stability and fate of submesoscale vortices in the ocean may be significantly modified by the presence of large-scale internal waves. This could in turn have a significant effect on the exchange of energy between the submesoscale and both larger and smaller scales.

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Anne-Marie E. G. Brunner-Suzuki, Miles A. Sundermeyer, and M.-Pascale Lelong

Abstract

Diapycnal mixing in the ocean is sporadic yet ubiquitous, leading to patches of mixing on a variety of scales. The adjustment of such mixed patches can lead to the formation of vortices and other small-scale geostrophic motions, which are thought to enhance lateral diffusivity. If vortices are densely populated, they can interact and merge, and upscale energy transfer can occur. Vortex interaction can also be modified by internal waves, thus impacting upscale transfer. Numerical experiments were used to study the effect of a large-scale near-inertial internal wave on a field of submesoscale vortices. While one might expect a vertical shear to limit the vertical scale of merging vortices, it was found that internal wave shear did not disrupt upscale energy transfer. Rather, under certain conditions, it enhanced upscale transfer by enhancing vortex–vortex interaction. If vortices were so densely populated that they interacted even in the absence of a wave, adding a forced large-scale wave enhanced the existing upscale transfer. Results further suggest that continuous forcing by the main driving mechanism (either vortices or internal waves) is necessary to maintain such upscale transfer. These findings could help to improve understanding of the direction of energy transfer in submesoscale oceanic processes.

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E. Kunze, J. M. Klymak, R.-C. Lien, R. Ferrari, C. M. Lee, M. A. Sundermeyer, and L. Goodman

Abstract

Submesoscale stirring contributes to the cascade of tracer variance from large to small scales. Multiple nested surveys in the summer Sargasso Sea with tow-yo and autonomous platforms captured submesoscale water-mass variability in the seasonal pycnocline at 20–60-m depths. To filter out internal waves that dominate dynamic signals on these scales, spectra for salinity anomalies on isopycnals were formed. Salinity-gradient spectra are approximately flat with slopes of −0.2 ± 0.2 over horizontal wavelengths of 0.03–10 km. While the two to three realizations presented here might be biased, more representative measurements in the literature are consistent with a nearly flat submesoscale passive tracer gradient spectrum for horizontal wavelengths in excess of 1 km. A review of mechanisms that could be responsible for a flat passive tracer gradient spectrum rules out (i) quasigeostrophic eddy stirring, (ii) atmospheric forcing through a relict submesoscale winter mixed layer structure or nocturnal mixed layer deepening, (iii) a downscale vortical-mode cascade, and (iv) horizontal diffusion because of shear dispersion of diapycnal mixing. Internal-wave horizontal strain appears to be able to explain horizontal wavenumbers of 0.1–7 cycles per kilometer (cpkm) but not the highest resolved wavenumbers (7–30 cpkm). Submesoscale subduction cannot be ruled out at these depths, though previous observations observe a flat spectrum well below subduction depths, so this seems unlikely. Primitive equation numerical modeling suggests that nonquasigeostrophic subinertial horizontal stirring can produce a flat spectrum. The last need not be limited to mode-one interior or surface Rossby wavenumbers of quasigeostrophic theory but may have a broaderband spectrum extending to smaller horizontal scales associated with frontogenesis and frontal instabilities as well as internal waves.

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M. A. Sundermeyer, E. A. Terray, J. R. Ledwell, A. G. Cunningham, P. E. LaRocque, J. Banic, and W. J. Lillycrop

Abstract

Results are presented from a pilot study using a fluorescent dye tracer imaged by airborne lidar in the ocean surface layer on spatial scales of meters to kilometers and temporal scales of minutes to hours. The lidar used here employs a scanning, frequency-doubled Nd:YAG laser to emit an infrared (1064 nm) and green (532 nm) pulse 6 ns in duration at a rate of 1 kHz. The received signal is split to infrared, green, and fluorescent (nominally 580–600 nm) channels, the latter two of which are used to compute absolute dye concentration as a function of depth and horizontal position. Comparison of dye concentrations inferred from the lidar with in situ fluorometry measurements made by ship shows good agreement both qualitatively and quantitatively for absolute dye concentrations ranging from 1 to >10 ppb. Uncertainties associated with horizontal variations in the natural seawater attenuation are approximately 1 ppb. The results demonstrate the ability of airborne lidar to capture high-resolution three-dimensional “snapshots” of the distribution of the tracer as it evolves over very short time and space scales. Such measurements offer a powerful observational tool for studies of transport and mixing on these scales.

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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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