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Abstract
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.
Abstract
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.
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.
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.
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.
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.
Abstract
A slab mixed layer model and two-dimensional numerical simulations are used to study the generation and energetics of near-inertial oscillations in a unidirectional, laterally sheared geostrophic current forced by oscillatory winds. The vertical vorticity of the current ζ
g
modifies the effective Coriolis frequency 
Abstract
A slab mixed layer model and two-dimensional numerical simulations are used to study the generation and energetics of near-inertial oscillations in a unidirectional, laterally sheared geostrophic current forced by oscillatory winds. The vertical vorticity of the current ζ
g
modifies the effective Coriolis frequency
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.
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.
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.
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.
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.
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.
Abstract
Using a process study model, the effect of mixed layer submesoscale instabilities on the lateral mixing of passive tracers in the pycnocline is explored. Mixed layer eddies that are generated from the baroclinic instability of a front within the mixed layer are found to penetrate into the pycnocline leading to an eddying flow field that acts to mix properties laterally along isopycnal surfaces. The mixing of passive tracers released on such isopycnal surfaces is quantified by estimating the variance of the tracer distribution over time. The evolution of the tracer variance reveals that the flow undergoes three different turbulent regimes. The first regime, lasting about 3–4 days (about 5 inertial periods) exhibits near-diffusive behavior; dispersion of the tracer grows nearly linearly with time. In the second regime, which lasts for about 10 days (about 14 inertial periods), tracer dispersion exhibits exponential growth because of the integrated action of high strain rates created by the instabilities. In the third regime, tracer dispersion follows Richardson’s power law. The Nakamura effective diffusivity is used to study the role of individual dynamical filaments in lateral mixing. The filaments, which carry a high concentration of tracer, are characterized by the coincidence of large horizontal strain rate with large vertical vorticity. Within filaments, tracer is sheared without being dispersed, and consequently the effective diffusivity is small in filaments. While the filament centers act as barriers to transport, eddy fluxes are enhanced at the filament edges where gradients are large.
Abstract
Using a process study model, the effect of mixed layer submesoscale instabilities on the lateral mixing of passive tracers in the pycnocline is explored. Mixed layer eddies that are generated from the baroclinic instability of a front within the mixed layer are found to penetrate into the pycnocline leading to an eddying flow field that acts to mix properties laterally along isopycnal surfaces. The mixing of passive tracers released on such isopycnal surfaces is quantified by estimating the variance of the tracer distribution over time. The evolution of the tracer variance reveals that the flow undergoes three different turbulent regimes. The first regime, lasting about 3–4 days (about 5 inertial periods) exhibits near-diffusive behavior; dispersion of the tracer grows nearly linearly with time. In the second regime, which lasts for about 10 days (about 14 inertial periods), tracer dispersion exhibits exponential growth because of the integrated action of high strain rates created by the instabilities. In the third regime, tracer dispersion follows Richardson’s power law. The Nakamura effective diffusivity is used to study the role of individual dynamical filaments in lateral mixing. The filaments, which carry a high concentration of tracer, are characterized by the coincidence of large horizontal strain rate with large vertical vorticity. Within filaments, tracer is sheared without being dispersed, and consequently the effective diffusivity is small in filaments. While the filament centers act as barriers to transport, eddy fluxes are enhanced at the filament edges where gradients are large.
