LatMix: Studies of Submesoscale Stirring and Mixing

Description:

Stirring and lateral mixing by submesoscale processes are believed to play an important role in setting the distribution of energy, vorticity, momentum, and tracers in the ocean, and their transfer from one scale to another. But an inadequate understanding of the underlying processes has limited our ability to reliably include their effects in general circulation models. The ONR Departmental Research Initiative, Scalable Lateral Mixing and Coherent Turbulence (LatMix), aimed to address this gap through intensive observations and modeling of these processes. The initiative included two field efforts in the vicinity of the Gulf Stream. In the first field campaign (June, 2011) three ships and an airborne LIDAR system examined processes in the seasonal pycnocline of the mesoscale eddy field just to the southeast of the Gulf Stream during relatively quiescent early summer conditions. The second campaign (February-March, 2012) was conducted from two ships in the core of the Gulf Stream in very dynamic late-winter conditions. Detailed field observations, along with high-resolution numerical modeling and remote sensing data, revealed a host of intricate mesoscale and submesoscale structures. Data analysis, theoretical work, and numerical simulations continue to elucidate a range of processes at scales of 0.1 to 10 km that lead to lateral mixing and energy transfer. This AMS special collection brings together papers presenting many of the results from this project. The overview article for this collection can be found here.

Collection organizers:
James R. Ledwell, Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution
Gualtiero Badin, Institute of Oceanography, University of Hamburg
Amala Mahadevan, Department of Physical Oceanography, Woods Hole Oceanographic Institution
Andrey Shcherbina, Applied Physics Laboratory, University of Washington, Seattle
Miles A. Sundermeyer, School for Marine Science and Technology, University of Massachusetts, Dartmouth

LatMix: Studies of Submesoscale Stirring and Mixing

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Jeffrey J. Early and Adam M. Sykulski

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A comprehensive method is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers that are typical in global positioning system (GPS) signals. We demonstrate the effectiveness of our methods on GPS trajectory data obtained from oceanographic floating instruments known as drifters.

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Ren-Chieh Lien and Thomas B. Sanford

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Twenty Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats in the upper-ocean thermocline of the summer Sargasso Sea observed the temporal and vertical variations of Ertel potential vorticity (PV) at 7–70-m vertical scale, averaged over O(4–8)-km horizontal scale. PV is dominated by its linear components—vertical vorticity and vortex stretching, each with an rms value of ~0.15f. In the internal wave frequency band, they are coherent and in phase, as expected for linear internal waves. Packets of strong, >0.2f, vertical vorticity and vortex stretching balance closely with a small net rms PV. The PV spectrum peaks at the highest resolvable vertical wavenumber, ~0.1 cpm. The PV frequency spectrum has a red spectral shape, a −1 spectral slope in the internal wave frequency band, and a small peak at the inertial frequency. PV measured at near-inertial frequencies is partially attributed to the non-Lagrangian nature of float measurements. Measurement errors and the vortical mode also contribute to PV in the internal wave frequency band. The vortical mode Burger number, computed using time rates of change of vertical vorticity and vortex stretching, is 0.2–0.4, implying a horizontal kinetic energy to available potential energy ratio of ~0.1. The vortical mode energy frequency spectrum is 1–2 decades less than the observed energy spectrum. Vortical mode energy is likely underestimated because its energy at vertical scales > 70 m was not measured. The vortical mode to total energy ratio increases with vertical wavenumber, implying its importance at small vertical scales.

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Jörn Callies and Raffaele Ferrari

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This paper revisits how the restratifying buoyancy flux generated by baroclinic mixed layer instabilities depends on environmental conditions. The frontal spindown is shown to produce buoyancy fluxes that increase significantly beyond the previously proposed and widely used scaling (f is the Coriolis parameter, Λ is the geostrophic shear, and H is the mixed layer depth), irrespective of whether the initial front is broad or narrow. This increase occurs after the initial phase of the nonlinear evolution, when the baroclinic eddies grow in size and develop velocities significantly in excess of the scaling assumption V ~ ΛH. Implications for parameterizing the restratification caused by baroclinic mixed layer instabilities in coarse-resolution models are discussed.

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Jörn Callies and Raffaele Ferrari

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Baroclinic mixed-layer instabilities have recently been recognized as an important source of submesoscale energy in deep winter mixed layers. While the focus has so far been on the balanced dynamics of these instabilities, they occur in and depend on an environment shaped by atmospherically forced small-scale turbulence. In this study, idealized numerical simulations are presented that allow the development of both baroclinic instability and convective small-scale turbulence, with simple control over the relative strength. If the convection is only weakly forced, baroclinic instability restratifies the layer and shuts off convection, as expected. With increased forcing, however, it is found that baroclinic instabilities are remarkably resilient to the presence of convection. Even if the instability is too weak to restratify the layer and shut off convection, the instability still grows in the convecting environment and generates baroclinic eddies and fronts. This suggests that despite the vigorous atmospherically forced small-scale turbulence in winter mixed layers, baroclinic instabilities can persistently grow, generate balanced submesoscale turbulence, and modify the bulk properties of the upper ocean.

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Daniel B. Whitt, Leif N. Thomas, Jody M. Klymak, Craig M. Lee, and Eric A. D’Asaro

Abstract

High-resolution, nearly Lagrangian observations of velocity and density made in the North Wall of the Gulf Stream reveal banded shear structures characteristic of near-inertial waves (NIWs). Here, the current follows submesoscale dynamics, with Rossby and Richardson numbers near one, and the vertical vorticity is positive. This allows for a unique analysis of the interaction of NIWs with a submesoscale current dominated by cyclonic as opposed to anticyclonic vorticity. Rotary spectra reveal that the vertical shear vector rotates primarily clockwise with depth and with time at frequencies near and above the local Coriolis frequency f. At some depths, more than half of the measured shear variance is explained by clockwise rotary motions with frequencies between f and 1.7f. The dominant superinertial frequencies are consistent with those inferred from a dispersion relation for NIWs in submesoscale currents that depends on the observed aspect ratio of the wave shear as well as the vertical vorticity, baroclinicity, and stratification of the balanced flow. These observations motivate a ray tracing calculation of superinertial wave propagation in the North Wall, where multiple filaments of strong cyclonic vorticity strongly modify wave propagation. The calculation shows that the minimum permissible frequency for inertia–gravity waves is mostly greater than the Coriolis frequency, and superinertial waves can be trapped and amplified at slantwise critical layers between cyclonic vortex filaments, providing a new plausible explanation for why the observed shear variance is dominated by superinertial waves.

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Callum J. Shakespeare and Leif N. Thomas

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Submesoscale-resolving numerical simulations are used to investigate a mechanism for sustained mode water formation via cabbeling at thermohaline fronts subject to a confluent strain flow. The simulations serve to further elucidate the mechanism and refine the predictions of the analytical model of Thomas and Shakespeare. Unlike other proposed mechanisms involving air–sea fluxes, the cabbeling mechanism, in addition to driving significant mode water formation, uniquely determines the thermohaline properties of the mode water given knowledge of the source water masses on either side of the front. The process of mode water formation in the simulations is as follows: Confluent flow associated with idealized mesoscale eddies forces water horizontally toward the front. The frontogenetic circulation draws this water near adiabatically from the full depth of the thermohaline front up to the surface 25 m, where resolved submesoscale instabilities drive intense mixing across the thermohaline front, creating the mode water. The mode water is denser than the surrounding stratified fluid and sinks to fill its neutral buoyancy layer at depth. This layer gradually expands up to the surface, and eddies composed entirely of this mode water detach from the front and accumulate in the diffluent regions of the domain. The process continues until the source water masses are exhausted. The temperature–salinity (TS) relation of the resulting mode water is biased to the properties of the source water that has the larger isopycnal TS anomaly. This mechanism has the potential to drive O(1) Sv (1 Sv ≡ 106 m3 s−1) mode water formation and may be important in determining the properties of mode water in the global oceans.

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Daniel Mukiibi, Gualtiero Badin, and Nuno Serra

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Three-dimensional (3D) finite-time Lyapunov exponents (FTLEs) are computed from numerical simulations of a freely evolving mixed layer (ML) front in a zonal channel undergoing baroclinic instability. The 3D FTLEs show a complex structure, with features that are less defined than the two-dimensional (2D) FTLEs, suggesting that stirring is not confined to the edges of vortices and along filaments and posing significant consequences on mixing. The magnitude of the FTLEs is observed to be strongly determined by the vertical shear. A scaling law relating the local FTLEs and the nonlocal density contrast used to initialize the ML front is derived assuming thermal wind balance. The scaling law only converges to the values found from the simulations within the pycnocline, while it displays differences within the ML, where the instabilities show a large ageostrophic component. The probability distribution functions of 2D and 3D FTLEs are found to be non-Gaussian at all depths. In the ML, the FTLEs wavenumber spectra display −1 slopes, while in the pycnocline, the FTLEs wavenumber spectra display −2 slopes, corresponding to frontal dynamics. Close to the surface, the geodesic Lagrangian coherent structures (LCSs) reveal a complex stirring structure, with elliptic structures detaching from the frontal region. In the pycnocline, LCSs are able to detect filamentary structures that are not captured by the Eulerian fields.

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Leif N. Thomas, John R. Taylor, Eric A. D’Asaro, Craig M. Lee, Jody M. Klymak, and Andrey Shcherbina

Abstract

The passage of a winter storm over the Gulf Stream observed with a Lagrangian float and hydrographic and velocity surveys provided a unique opportunity to study how the interaction of inertial oscillations, the front, and symmetric instability (SI) shapes the stratification, shear, and turbulence in the upper ocean under unsteady forcing. During the storm, the rapid rise and rotation of the winds excited inertial motions. Acting on the front, these sheared motions modulate the stratification in the surface boundary layer. At the same time, cooling and downfront winds generated a symmetrically unstable flow. The observed turbulent kinetic energy dissipation exceeded what could be attributed to atmospheric forcing, implying SI drew energy from the front. The peak excess dissipation, which occurred just prior to a minimum in stratification, surpassed that predicted for steady SI turbulence, suggesting the importance of unsteady dynamics. The measurements are interpreted using a large-eddy simulation (LES) and a stability analysis configured with parameters taken from the observations. The stability analysis illustrates how SI more efficiently extracts energy from a front via shear production during periods when inertial motions reduce stratification. Diagnostics of the energetics of SI from the LES highlight the temporal variability in shear production but also demonstrate that the time-averaged energy balance is consistent with a theoretical scaling that has previously been tested only for steady forcing. As the storm passed and the winds and cooling subsided, the boundary layer restratified and the thermal wind balance was reestablished in a manner reminiscent of geostrophic adjustment.

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Eric Kunze and Miles A. Sundermeyer

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This paper revisits a long-standing discrepancy between (i) 1–5-km isopycnal diffusivities of O(1) m2 s−1 based on dye spreading and (ii) inferences of O(0.1) m2 s−1 from internal-wave shear dispersion K h ~ 〈K z〉〈〉/f 2 in several studies in the stratified ocean interior, where 〈K z〉 is the bulk average diapycnal diffusivity, 〈〉 the finescale shear variance, and f the Coriolis frequency. It is shown that, taking into account (i) the intermittency of shear-driven turbulence, (ii) its lognormality, and (iii) its correlation with unstable finescale near-inertial shear, internal-wave shear dispersion cannot necessarily be discounted based on available information. This result depends on an infrequent occurrence of turbulence bursts, as is observed, and a correlation between diapycnal diffusivity K z and the off-diagonal vertical strain, or the vertical gradient of horizontal displacement, |χ z| = |∫V z dt|, which is not well known and may vary from region to region. Taking these factors into account, there may be no need to invoke additional submesoscale mixing mechanisms such as vortical-mode stirring or internal-wave Stokes drift to explain the previously reported discrepancies.

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Leif N. Thomas and Callum J. Shakespeare

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A simple analytical model is used to elucidate a potential mechanism for steady-state mode water formation at a thermohaline front that involves frontogenesis, submesoscale lateral mixing, and cabbeling. This mechanism is motivated in part by recent observations of an extremely sharp, density-compensated front at the North Wall of the Gulf Stream. Here, the intergyre, along-isopycnal, salinity–temperature difference is compressed into a span of a few kilometers, making the flow susceptible to cabbeling. The sharpness of the front is caused by frontogenetic strain, which is presumably balanced by submesoscale lateral mixing processes. The balance is studied with the simple model, and a scaling is derived for the amount of water mass transformation resulting from the ensuing cabbeling. The transformation scales with the strain rate, equilibrated width of the front, and the square of the isopycnal temperature contrast across the front. At the major ocean fronts where mode waters are found, this isopycnal temperature contrast decreases with increasing density near the isopycnal layers where mode waters reside. This implies that cabbeling should result in a convergent diapycnal mass flux into mode water density classes. The scaling for the transformation suggests that at these fronts the process could generate 0.01–1 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) of mode water. These formation rates, while smaller than mode water formation by air–sea fluxes, should be independent of season and thus could fill select isopycnal layers continuously and play an important role in the dynamics of mode waters on interannual time scales.

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