Gualtiero Badin

The latmix summer campaign: Submesoscale stirring in the upper ocean

AbstractLateral 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 diff...

Lateral Mixing in the Pycnocline by Baroclinic Mixed Layer Eddies

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 instabilityofafrontwithinthemixedlayerarefoundtopenetrate intothepycnoclineleadingtoaneddyingflow 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.

Surface semi-geostrophic dynamics in the ocean

The surface quasi-geostrophic approximation is re-written in an oceanic context using the two-dimensional semi-geostrophic approximation. The new formulation allows to take into account the presence of out-of-balance flow features at scales comparable to or smaller than the Rossby radius of deformation and for small bulk Richardson numbers. Analytical solutions show that, while the surface quasi-geostrophic approximation tends to underestimate the buoyancy anomaly, the inclusion of finite Rossby number allows for larger values of the buoyancy anomaly at depth. The projection of the surface semi-geostrophic solution on the first baroclinic modes is calculated. The result of the projection is a functional form that decreases with the values of the Rossby number and toward smaller scales. Solutions for constant and exponential profile for the background potential vorticity are compared. Results of the comparison show that, in agreement with the results found for balanced flows, even for large Rossby number the exponential profile for the background potential vorticity retains smaller values for the buoyancy anomaly at depth than the solution found using a constant potential vorticity profile. †Previously at: Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA.

On the Buoyancy Forcing and Residual Circulation in the Southern Ocean: The Feedback from Ekman and Eddy Transfer

The effect of buoyancy forcing on the residual circulation in the Southern Ocean is examined in two different ways. First, the rates of water-mass transformation and formation are estimated using air‐sea fluxes of heat and freshwater in the isopycnal framework developed by Walin, which is applied to two different air‐sea flux climatologies and a reanalysis dataset. In the limit of no diabatic mixing and at a steady state, these air‐sea flux estimates of water-mass transformation and formation are equivalent to estimating the residual circulation and the subduction rates in the upper ocean, respectively. All three datasets reveal a transformation of dense to light waters between s 5 26.8 and 27.2, as well as positive formation rates peaking at s 5 26.6, versus negative rates peaking at s 5 27. The transformation is achieved either by surface heating or freshwater inputs, although the magnitude of the formation rates varies in each case. Second, an idealized model of a mixed layer and adiabatic thermocline for a channel is used to illustrate how changes in ocean dynamics in the mixed layer and freshwater fluxes can modify the buoyancy fluxes and, thus, alter the residual circulation. Increasing the Ekman advection of cold water northward enhances the air‐sea temperature difference and the surface heat flux into the ocean, which then increases the residual circulation; an increase in wind stress of 0.05 N m 22 typically increases the surface heat flux by 8 W m 22 and alters the peaks in formation rate by up to 8 Sv (1 Sv [ 10 6 m 3 s 21 ). Conversely, increasing the eddy advection and diffusion leads to an opposing weaker effect; an increase in the eddy transfer coefficient of 500 m 2 s 21 decreases the surface heat flux by 3Wm 22 and alters the peaks in formation rate by 1 Sv.

Water Mass Transformations in the Southern Ocean Diagnosed from Observations: Contrasting Effects of Air–Sea Fluxes and Diapycnal Mixing

AbstractTransformation and formation rates of water masses in the Southern Ocean are estimated in a neutral-surface framework using air–sea fluxes of heat and freshwater together with in situ estimates of diapycnal mixing. The air–sea fluxes are taken from two different climatologies and a reanalysis dataset, while the diapycnal mixing is estimated from a mixing parameterization applied to five years of Argo float data. Air–sea fluxes lead to a large transformation directed toward lighter waters, typically from −45 to −63 Sv (1 Sv ≡ 106 m3 s−1) centered at γ = 27.2, while interior diapycnal mixing leads to two weaker peaks in transformation, directed toward denser waters, 8 Sv centered at γ = 27.8, and directed toward lighter waters, −16 Sv centered at γ = 28.3. Hence, air–sea fluxes and interior diapycnal mixing are important in transforming different water masses within the Southern Ocean. The transformation of dense to lighter waters by diapycnal mixing within the Southern Ocean is slightly larger, tho...

Water-mass transformation in the shelf seas

The rate at which water masses are transformed from one density class to another is assessed in the shelf seas using the Walin (1982) framework. For a tidal-mixing front, the transformation is estimated using air-sea density fluxes and the diapycnal mixing diagnosed from a series of one-dimensional mixed layer models running across the shelf. These transformation rates diagnosed from the air-sea fluxes and diapycnal mixing agree with volume changes dagnosed directly from the model. The transformation from air-sea fluxes reaches a maximum amplitude typically twice that provided by diffusive mixing. This framework is extended to estimate the rate at which nutrients are converted in nutrient space including the effects of biological consumption. The transformation in density and nutrient space are broadly related in the spring when there is a relatively tight relationship between density and nutrient concentrations. For a shelf-break front in the Celtic Seas, the transformation is estimated from a combination of observed air-sea fluxes, remotely-sensed sea surface temperature and ship-based measurements of density and turbulent mixing. The transformation is controlled by diapycnal mixing along dense surfaces and by air-sea fluxes for lighter surfaces, and each contribution reaches comparable magnitudes over a six-month period

Hydrodynamic Nambu brackets derived by geometric constraints

A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an orthogonality condition. As a result, 2D hydrodynamics with vorticity as dynamic variable emerges as a generic model, with conservation laws which can be interpreted as enstrophy and energy functionals. Generalized forms like surface quasi-geostrophy and fractional Poisson equations for the stream-function are also included as results from the derivation. The formalism is extended to a hydrodynamic system coupled to a second degree of freedom, with the Rayleigh–Benard convection as an example. This system is reformulated in terms of constitutive conservation laws with two additive brackets which represent individual processes: a first representing inviscid 2D hydrodynamics, and a second representing the coupling between hydrodynamics and thermodynamics. The results can be used for the formulation of conservative numerical algorithms that can be employed, for example, for the study of fronts and singularities.

On the role of non-uniform stratification and short-wave instabilities in three-layer quasi-geostrophic turbulence

The role of short-wave instabilities on geostrophic turbulence is studied in a simplified model consisting of three layers in the quasi-geostrophic approximation. The linear stability analysis shows that short-wave instabilities are created by the interplay between the shear in the upper and lower layers. If the stratification is non-uniform, in particular surface intensified, the linear growth rate is larger for short-wave instabilities than for long-wave instabilities and the layers are essentially decoupled, with the small scales growing independently. The fully developed homogeneous turbulence is studied in a number of numerical experiments. Results show that in both the case of equal layer depths and surface intensified stratification an inverse cascade in kinetic energy is observed. The modal kinetic energy spectra for the case with surface intensified stratification show higher energy for higher baroclinic numbers at small scales, due to the decoupling of the layers. As a result, while the case wit...

A Search for Chaotic Behavior in Northern Hemisphere Stratospheric Variability

AbstractNorthern Hemisphere stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products and two numerical model runs with different forcing. The time series show red spectra at all frequencies and the probability distribution functions show persistent deviations from a Gaussian distribution. An exception is given by the numerical model forced with perpetual winter conditions—a case that shows more variability and follows a Gaussian distribution, suggesting that the deviation from Gaussianity found in the observations is due to the transition between summer and winter variability. To search for the presence of a chaotic attractor the correlation dimension and entropy, the Lyapunov spectrum, and the associated Kaplan–Yorke dimension are estimated. A finite value of the dimensions can be computed for each variable and data product, with the correlation dimension ranging between 3.0 and 4.0 and th...

Three-Dimensional Chaotic Advection by Mixed Layer Baroclinic Instabilities

AbstractThree-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 wavenumb...