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Leif N. Thomas

Abstract

The destruction of potential vorticity (PV) at ocean fronts by wind stress–driven frictional forces is examined using PV flux formalism and numerical simulations. When a front is forced by “downfront” winds, that is, winds blowing in the direction of the frontal jet, a nonadvective frictional PV flux that is upward at the sea surface is induced. The flux extracts PV out of the ocean, leading to the formation of a boundary layer thicker than the Ekman layer, with nearly zero PV and nonzero stratification. The PV reduction is not only active in the Ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low PV from the Ekman layer with high PV from the pycnocline. Extraction of PV from the pycnocline by the secondary circulations results in an upward advective PV flux at the base of the boundary layer that scales with the surface, nonadvective, frictional PV flux and that leads to the deepening of the layer. At fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux FB atm, the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for PV destruction is (H/δe)(FB wind/FB atm), where H and δe are the mixed layer and Ekman layer depths, FB wind = S 2 τo/(ρof ), S 2 is the magnitude of the lateral buoyancy gradient of the front, τo is the downfront component of the wind stress, ρo is a reference density, and f is the Coriolis parameter. When this parameter is greater than 1, PV destruction by winds dominates and may play an important role in the formation of mode water.

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Leif N. Thomas

Abstract

Near-inertial waves (NIWs) radiate energy out of the mixed layer when they develop small lateral scales. Refraction of these waves by gradients in planetary and vertical vorticity has traditionally been invoked to explain this phenomenon. Here, a new mechanism for the enhancement of NIW radiation is described involving the interaction of NIWs with vertical circulations at fronts undergoing frontogenesis. Frontal vertical circulations drive a Doppler shift that is proportional to the wave’s vertical wavenumber m and that changes sign across a front, inducing large lateral differences in wave phase within a few inertial periods. Theory predicts that the process should generate a vertical energy flux that varies inversely with m in contrast to the m −3 dependence expected from refraction. As a consequence, high-mode NIWs are much more effective at radiating energy when fronts and their vertical circulation are present. Numerical simulations initialized with fronts, an array of eddies that drive frontogenesis, and NIWs of various modes are used to test the theory. In the simulations, the interaction of the NIWs with the frontal vertical circulations generates wave beams that radiate down from the fronts. The resultant downward energy flux varies with m following the theoretical scaling laws. In the beams, the Eulerian frequency is inertial within a few percent, yet the waves’ potential and kinetic energies are comparable, thus indicating a superinertial intrinsic frequency. The downshift in Eulerian frequency from the intrinsic frequency is due to horizontal advection of the waves by the eddies.

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Nicolas Grisouard and Leif N. Thomas

Abstract

Inertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.

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Jessica Benthuysen and Leif N. Thomas

Abstract

Although atmospheric forcing by wind stress or buoyancy flux is known to change the ocean’s potential vorticity (PV) at the surface, less is understood about PV modification in the bottom boundary layer. The adjustment of a geostrophic current over a sloped bottom in a stratified ocean generates PV sources and sinks through friction and diapycnal mixing. The time-dependent problem is solved analytically for a no-slip boundary condition, and scalings are identified for the change in PV that arises during the adjustment to steady state. Numerical experiments are run to test the scalings with different turbulent closure schemes. The key parameters that control whether PV is injected into or extracted from the fluid are the direction of the geostrophic current and the ratio of its initial speed to its steady-state speed. When the current is in the direction of Kelvin wave propagation, downslope Ekman flow advects lighter water under denser water, driving diabatic mixing and extracting PV. For a current in the opposite direction, Ekman advection tends to restratify the bottom boundary layer and increase the PV. Mixing near the bottom counteracts this restratification, however, and an increase in PV will only occur for current speeds exceeding a critical value. Consequently, the change in PV is asymmetric for currents of the opposite sign but the same speed, with a bias toward PV removal. In the limit of a large speed ratio, the change in PV is independent of diapycnal mixing.

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Leif N. Thomas and Terrence M. Joyce

Abstract

Sections of temperature, salinity, dissolved oxygen, and velocity were made crossing the Gulf Stream in late January 2006 to investigate the role of frontal processes in the formation of Eighteen Degree Water (EDW), the Subtropical Mode Water of the North Atlantic. The sections were nominally perpendicular to the stream and measured in a Lagrangian frame by following a floating spar buoy drifting in the Gulf Stream’s warm core. During the survey, EDW was isolated from the mixed layer by the stratified seasonal pycnocline, suggesting that EDW was not yet actively being formed at this time in the season and at the longitudes over which the survey was conducted (64°–70°W). However, in two of the sections, the seasonal pycnocline in the core of the Gulf Stream was broken by an intrusion of cold, fresh, weakly stratified water, nearly saturated in oxygen, that appears to have been subducted from the surface mixed layer north of the stream. The intrusion was identified in three of the sections in profiles with a nearly identical temperature–salinity relation. From the western-to-easternmost sections, where the intrusion was observed, the depth of the intrusion’s salinity minimum descended by ∼90 m in the 71 h it took to complete this part of the survey. This apparent subduction occurred primarily on the upstream side of a meander trough, where the cross-stream velocity was confluent and frontogenetic. Using a variant of the omega equation, the vertical velocity driven by the confluent flow was inferred and yielded downwelling in the vicinity of the intrusion spanning 10–40 m day−1, a range of values consistent with the intrusion’s observed descent, suggesting that frontal subduction was responsible for the formation of the intrusion. In the easternmost section located downstream of the meander trough, the flow was diffluent, driving an inferred vertical circulation that was of the opposite sense to that in the section upstream of the trough. In transiting the two sides of the trough, the intrusion was observed to move toward the center of the stream between the downwelling branches of the opposing vertical circulations, resulting in a downward Lagrangian mean vertical velocity and net subduction. Hydrographic evidence of the subduction of weakly stratified surface waters was seen in the southern flank of the Gulf Stream as well. The solution of the omega equation suggests that this subduction was associated with a relatively shallow vertical circulation confined to the upper 200 m of the water column in the proximity of the front marking the southern edge of the warm core.

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Callum J. Shakespeare and Leif N. Thomas

Abstract

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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Leif N. Thomas and Callum J. Shakespeare

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.

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Daniel B. Whitt and Leif N. Thomas

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An analysis and physical interpretation of near-inertial waves (NIWs) propagating perpendicular to a steady, two-dimensional, strongly baroclinic, geostrophic current are presented. The analysis is appropriate for geostrophic currents with order-one Richardson numbers such as those associated with fronts experiencing strong, wintertime atmospheric forcing. This work highlights the underlying physics behind the properties of the NIWs using parcel arguments and the principles of conservation of density and absolute momentum. Baroclinicity introduces lateral gradients in density and vertical gradients in absolute momentum that significantly modify the dispersion and polarization relations and propagation of NIWs relative to classical internal wave theory. In particular, oscillations at the minimum frequency are not horizontal but, instead, are slanted along isopycnals. Furthermore, the polarization of the horizontal velocity is not necessarily circular at the minimum frequency and the spiraling of the wave’s velocity vector with time and depth can be in the opposite direction from that predicted by classical theory. Ray tracing and numerical solutions illustrate the trapping and amplification of NIWs in regions of strong baroclinicity where the wave frequency is lower than the effective Coriolis frequency. The largest amplification is found at slantwise critical layers that align with the tilted isopycnals of the current. Such slantwise critical layers are seen in wintertime observations of the Gulf Stream and, consistent with the theory, coincide with regions of intensified ageostrophic shear characterized by a banded structure that is spatially coherent along isopycnals.

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Daniel B. Whitt and Leif N. Thomas

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 , which is equivalent to the local resonant forcing frequency. In addition, the resonant oscillatory velocity response is elliptical, not circular, because the oscillation periodically exchanges energy with the geostrophic flow via shear production. With damping, this energy exchange becomes permanent, but its magnitude and sign depend strongly on the angle of the oscillatory wind vector relative to the geostrophic flow. However, for a current forced by an isotropic distribution of wind directions, the response averaged over all wind angles results in a net extraction of energy from the geostrophic flow that scales as the wind work on the inertial motions times (ζ g/f)2 for ζ gf. For ζ g ~ f, this sink of geostrophic kinetic energy preferentially damps flows with anticyclonic vorticity and thus could contribute toward shaping the positively skewed vorticity distribution observed in the upper ocean.

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Jacob O. Wenegrat and Leif N. Thomas

Abstract

Flow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.

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