Andreas Klocker

Influence of the Nonlinear Equation of State on Global Estimates of Dianeutral Advection and Diffusion

Abstract Recent work on the global overturning circulation and its energetics assumes that processes caused by nonlinearities of the equation of state of seawater are negligible. Nonlinear processes such as cabbeling and thermobaricity cause diapycnal motion as a consequence of isopycnal mixing. The nonlinear equation of state also causes the helical nature of neutral trajectories; as a consequence of this helical nature, it is not possible to define a continuous “density” surface that aligns with neutral tangent planes. The result is an additional diapycnal advection, which needs to be accounted for in water-mass analysis. In this paper, the authors take advantage of new techniques in constructing very accurate continuous density surfaces to more precisely estimate isopycnal and diapycnal processes caused by the nonlinear equation of state. They then quantify the diapycnal advection due to each of these nonlinear processes and show that they lead in total to a significant downward diapycnal advection, pa...

Global Patterns of Mesoscale Eddy Properties and Diffusivities

Mesoscale eddies play a major role in the transport of tracers in the ocean. Focusing on a sector in the east Pacific, the authors present estimates of eddy diffusivities derived from kinematic tracer simulations using satellite-observed velocity fields. Meridional diffusivities are diagnosed, and how they are related to eddy properties through the mixing length formulation of Ferrari and Nikurashin, which accounts for the suppression of diffusivity due to eddy propagation relative to the mean flow, is shown. The uniqueness of this studyis that, throughsystematically varyingthe zonal-meanflow, a hypothetical ‘‘unsuppressed’’ diffusivity is diagnosed. At a given latitude, the unsuppressed diffusivity occurs when the zonal-mean flow equals the eddy phase speed. This provides an independent estimate of eddy phase propagation, which agrees well with theoretical arguments. It is also shown that the unsuppressed diffusivity is predicted very well by classical mixing length theory, that is, that it is proportional to the rms eddy velocity times the observed eddy size, with a spatially constant mixing efficiency of 0.35. Then, the suppression factor is estimated and it is shown that it too can be understood quantitatively in terms of easily observed mean flow properties. The authors then extrapolate from these sector experiments to the global scale, making predictions for the global surface eddy diffusivity. Together with a prognostic equation for eddy kinetic energy and a theory explaining observed eddy sizes, these concepts could potentially be used in a closure for eddy diffusivities in coarse-resolution ocean climate models.

Estimating suppression of eddy mixing by mean flows

Particle- and tracer-based estimates of lateral diffusivities are used to estimate the suppression of eddy mixingacrossstrongcurrents.Particlesandtracersare advectedusingavelocityfieldderivedfromseasurface height measurements from the South Pacific, in a region west of Drake Passage. This velocity field has been used in a companion paper to show that both particle- and tracer-based estimates of eddy diffusivities are equivalent, despite recent claims to the contrary. These estimates of eddy diffusivities are here analyzed to show 1) that the degree of suppression of mixing across the strong Antarctic Circumpolar Current is correctly predicted by mixing length theory modified to include eddy propagation along the mean flow and 2) that the suppressioncan beinferredfromparticletrajectoriesby studyingthestructureofthe autocorrelationfunction of the particle velocities beyond the first zero crossing. These results are then used to discuss how to compute lateral and vertical variations in eddy diffusivities using floats and drifters in the real ocean.

Direct estimate of lateral eddy diffusivity upstream of Drake Passage

AbstractThe first direct estimate of the rate at which geostrophic turbulence mixes tracers across the Antarctic Circumpolar Current is presented. The estimate is computed from the spreading of a tracer released upstream of Drake Passage as part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). The meridional eddy diffusivity, a measure of the rate at which the area of the tracer spreads along an isopycnal across the Antarctic Circumpolar Current, is 710 ± 260 m2 s−1 at 1500-m depth. The estimate is based on an extrapolation of the tracer-based diffusivity using output from numerical tracers released in a one-twentieth of a degree model simulation of the circulation and turbulence in the Drake Passage region. The model is shown to reproduce the observed spreading rate of the DIMES tracer and suggests that the meridional eddy diffusivity is weak in the upper kilometer of the water column with values below 500 m2 s−1 and peaks at the steering level, near 2 km, where the eddy ph...

The Deep Ocean Buoyancy Budget and Its Temporal Variability

AbstractDespite slow rates of ocean mixing, observational and modeling studies suggest that buoyancy is redistributed to all depths of the ocean on surprisingly short interannual to decadal time scales. The mechanisms responsible for this redistribution remain poorly understood. This work uses an Earth system model to evaluate the global steady-state ocean buoyancy (and related steric sea level) budget, its interannual variability, and its transient response to a doubling of CO2 over 70 years, with a focus on the deep ocean. At steady state, the simple view of vertical advective–diffusive balance for the deep ocean holds at low to midlatitudes. At higher latitudes, the balance depends on a myriad of additional terms, namely mesoscale and submesoscale advection, convection and overflows from marginal seas, and terms related to the nonlinear equation of state. These high-latitude processes rapidly communicate anomalies in surface buoyancy forcing to the deep ocean locally; the deep, high-latitude changes th...

Advection of baroclinic eddies by depth mean flow

Observed zonal propagation speeds of nonlinear eddies, derived using an eddy tracking algorithm, are compared with the classical long Rossby wave speed, Doppler shifted by just the depth mean velocity, the latter obtained from annual mean hydrography and an ocean atlas. Despite neglecting any Doppler shift from baroclinic background flows, the correspondence between observed eddy propagation speeds and theoretical long Rossby wave phase speeds is improved in the Antarctic Circumpolar Current region, where both show eastward propagation at speeds of 1–3 cm s−1, although the observed eastward eddy propagation speeds are systematically lower than the predicted Rossby wave phase speeds.

Quantifying the Consequences of the Ill-Defined Nature of Neutral Surfaces

Abstract In the absence of diapycnal mixing processes, fluid parcels move in directions along which they do not encounter buoyant forces. These directions define the local neutral tangent plane. Because of the nonlinear nature of the equation of state of seawater, these neutral tangent planes cannot be connected globally to form a well-defined surface in three-dimensional space; that is, continuous “neutral surfaces” do not exist. This inability to form well-defined neutral surfaces implies that neutral trajectories are helical. Consequently, even in the absence of diapycnal mixing processes, fluid trajectories penetrate through any “density” surface. This process amounts to an extra mechanism that achieves mean vertical advection through any continuous surface such as surfaces of constant potential density or neutral density. That is, the helical nature of neutral trajectories causes this additional diasurface velocity. A water-mass analysis performed with respect to continuous density surfaces will have...

Water Mass Transformation by Cabbeling and Thermobaricity

Water mass transformation is an important process for the global ocean circulation. Nonlinearities in the equation of state of seawater lead to water mass transformation due to cabbeling and thermobaricity. Here, the contribution of cabbeling and thermobaricity to water mass transformation is calculated in a Neutral Density framework, using temperature gradients derived from observationally-based gridded climatologies and observationally-based estimates of the spatially varying eddy diffusivities. It is shown that cabbeling and thermobaricity play a significant role in the water-mass transformation budget, with cabbeling having a particularly important role in the formation of Antarctic Intermediate Water and Antarctic Bottom Water. A physical hypothesis is presented which explains why cabbeling is important for Antarctic Intermediate Water formation. It is shown that spatially varying estimates of eddy diffusivities are essential to correctly quantify the role of cabbeling to the formation of Antarctic Intermediate Water.

Planetary-geometric constraints on isopycnal slope in the Southern Ocean

AbstractOn planetary scales, surface wind stress and differential buoyancy forcing act together to produce isopycnal surfaces that are relatively flat in the tropics/subtropics and steep near the poles, where they tend to outcrop. Tilted isopycnals in a rapidly rotating fluid are subject to baroclinic instability. The turbulent, mesoscale eddies generated by this instability have a tendency to homogenize potential vorticity (PV) along density surfaces. In the Southern Ocean (SO), the tilt of isopycnals is largely maintained by competition between the steepening effect of surface forcing and the flattening effect of turbulent, spatially inhomogeneous eddy fluxes of PV. Here quasigeostrophic theory is used to investigate the influence of a planetary–geometric constraint on the equilibrium slope of tilted density/buoyancy surfaces in the SO. If the meridional gradients of relative vorticity and PV are small relative to β, then quasigeostrophic theory predicts ds/dz = β/f0 = cot(ϕ0)/a, or equivalently r ≡ |∂z...

Opening the window to the Southern Ocean: The role of jet dynamics

Jet dynamics play a crucial role in Southern Ocean ventilation. The surface waters of the Southern Ocean act as a control valve through which climatically important tracers such as heat, freshwater, and CO2 are transferred between the atmosphere and the ocean. The process that transports these tracers through the surface mixed layer into the ocean interior is known as ocean ventilation. Changes in ocean ventilation are thought to be important for both rapid transitions of the ocean’s global overturning circulation during the last deglaciation and the uptake and storage of excess heat and CO2 as a consequence of anthropogenic climate change. I show how the interaction between Southern Ocean jets, topographic features, and ocean stratification can lead to rapid changes in Southern Ocean ventilation as a function of wind stress. For increasing winds, this interaction leads from a state in which tracers are confined to the surface mixed layer to a state in which tracers fill the ocean interior. For sufficiently high winds, the jet dynamics abruptly change, allowing the tracer to ventilate a water mass known as Antarctic Intermediate Water in the mid-depth Southern Ocean. Abrupt changes in Antarctic Intermediate Water ventilation have played a major role in rapid climate transitions in Earth’s past, and combined with the results presented here, this would suggest that jet dynamics could play a prominent role in contributing to, or even triggering, rapid transitions of the global climate system.