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M-Pascale Lelong and Timothy J. Dunkerton

Abstract

The three-dimensional breakdown of a large-amplitude, convectively unstable inertia–gravity wave is examined numerically as a function of primary-wave frequency and amplitude. The results confirm that near-inertial waves break down preferentially via shear instability even when the primary wave is initially overturned. As in the convectively stable near-inertial regime, the spectrum of instability energy is approximately isotropic in azimuthal orientation. At intermediate frequencies, wave breakdown is triggered by a transverse shear instability in the region of overturning. This behavior, displaying a clear preference for instability with horizontal component of wavevector in the transverse direction, is different from the breakdown of convectively stable waves at intermediate frequency examined in Part I. As the primary-wave frequency is increased further, shear instabilities once again develop in the transverse direction, but they are modified by convective instability as the billows reach finite amplitude. The influence of transverse vertical shear becomes progressively weaker as the wave frequency approaches the buoyancy frequency. In this limit, transverse convection leads to wave collapse, and there is no preferred scale of instability.

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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 Timothy J. Dunkerton

Abstract

The three-dimensional breakdown of a large-amplitude, convectively stable inertia–gravity wave is examined numerically as a function of primary-wave frequency and amplitude. The results confirm that inertia–gravity waves in this region of parameter space break down preferentially via shear instability. In low-frequency waves the instability is ubiquitous, occurring simultaneously throughout the wave field, and the spectrum of instability energy is approximately, but not exactly, isotropic in azimuthal orientation. In higher-frequency waves, shear instability develops adjacent to the region of reduced static stability, and displays a preference for intermediate azimuths (e.g., near 45°). Near-inertial waves experience the fastest growing instabilities. The growth rate of shear instability drops off rapidly as the wave frequency is increased and, for all frequencies, increases with increasing wave amplitude. At most frequencies, the onset of modal shear instability occurs at a wave amplitude slightly above the theoretical stability boundary determined from a local Richardson number argument.

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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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Pascale Bouruet-Aubertot, Hans van Haren, and M. Pascale Lelong

Abstract

Deep-ocean high-resolution moored temperature data are analyzed with a focus on superbuoyant frequencies. A local Taylor hypothesis based on the horizontal velocity averaged over 2 h is used to infer horizontal wavenumber spectra of temperature variance. The inertial subrange extends over fairly low horizontal wavenumbers, typically within 2 × 10−3 and 2 × 10−1 cycles per minute (cpm). It is therefore interpreted as a stratified inertial subrange for most of this wavenumber interval, whereas in some cases the convective inertial subrange is resolved as well. Kinetic energy dissipation rate ϵ is inferred using theoretical expressions for the stratified inertial subrange. A wide range of values within 10−9 and 4 × 10−7 m2 s−3 is obtained for time periods either dominated by semidiurnal tides or by significant subinertial variability. A scaling for ϵ that depends on the potential energy within the inertio-gravity waves (IGW) frequency band PEIGW and the buoyancy frequency N is proposed for these two cases. When semidiurnal tides dominate, ϵ ≃ (PEIGW N)3/2, whereas ϵ ≃ PEIGW N in the presence of significant subinertial variability. This result is obtained for energy levels ranging from 1 to 30 times the Garrett–Munk energy level and is in contrast with classical finescale parameterization in which ϵ ∼ (PEIGW)2 that applies far from energy sources. The specificities of the stratified bottom boundary layer, namely a weak stratification, may account for this difference.

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M.-Pascale Lelong, Yannis Cuypers, and Pascale Bouruet-Aubertot

Abstract

Motivated by observations of a strong near-inertial wave signal at the base of the semipermanent anticyclonic Cyprus Eddy during the 2010 Biogeochemistry from the Oligotrophic to the Ultraoligotrophic Mediterranean (BOUM) experiment, a numerical study is performed to investigate the role of near-inertial/eddy interactions in energy transfer out of the mixed layer. A hybrid temporal–spatial decomposition is used to split all variables into three independent components: slow (eddy) and fast (inertial oscillations + waves), which proves useful in understanding the flow dynamics. Through a detailed energy budget analysis, we find that the anticyclonic eddy acts as a catalyst in transferring wind-driven inertial energy to propagating waves. While the eddy sets the spatial scales of the waves, it does not participate in any energy exchange. Near-inertial propagation through the eddy core results in the formation of multiple critical levels with the largest accumulation of wave energy at the base of the eddy. A complementary ray-tracing analysis reveals critical-level formation when the surface-confined inertial rays originate within the negative vorticity region. In contrast, rays originating outside this region focus at the base of the eddy and can propagate at depth.

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Angelique C. Haza, Tamay M. Özgökmen, Annalisa Griffa, Andrew C. Poje, and M.-Pascale Lelong

Abstract

To develop methodologies to maximize the information content of Lagrangian data subject to position errors, synthetic trajectories produced by both a large-eddy simulation (LES) of an idealized submesoscale flow field and a high-resolution Hybrid Coordinate Ocean Model simulation of the North Atlantic circulation are analyzed. Scale-dependent Lagrangian measures of two-particle dispersion, mainly the finite-scale Lyapunov exponent [FSLE; λ(δ)], are used as metrics to determine the effects of position uncertainty on the observed dispersion regimes. It is found that the cumulative effect of position uncertainty on λ(δ) may extend to scales 20–60 times larger than the position uncertainty. The range of separation scales affected by a given level of position uncertainty depends upon the slope of the true FSLE distribution at the scale of the uncertainty. Low-pass filtering or temporal subsampling of the trajectories reduces the effective noise amplitudes at the smallest spatial scales at the expense of limiting the maximum computable value of λ. An adaptive time-filtering approach is proposed as a means of extracting the true FSLE signal from data with uncertain position measurements. Application of this filtering process to the drifters with the Argos positioning system released during the LatMix: Studies of Submesoscale Stirring and Mixing (2011) indicates that the measurement noise dominates the dispersion regime in λ for separation scales δ < 3 km. An expression is provided to estimate position errors that can be afforded depending on the expected maximum λ in the submesoscale regime.

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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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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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