ALBERT

Description: Eastward zonal jets are common in the ocean and atmosphere, for example, the Gulf Stream and jet stream. They are characterized by atypically strong horizontal velocity, baroclinic vertical structure with an upward flow intensification, large change in the density stratification meridionally across the jet, large-scale meanders around a central latitude, narrow troughs and broad crests, and a sharp and vertically sloping northern (poleward) “wall” defined by horizontal maxima in the lateral gradients of both velocity and density. Measurements and realistic oceanic simulations show these features in the Gulf Stream downstream from its western boundary separation point. A diagnostic theory based on the conservative balance equations is developed to calculate the 3D velocity field associated with the dynamic height field. When applied to an idealized representation of a meandering jet, it explains the spatial structure of the associated ageostrophic secondary circulation around the jet and the positive frontogenetic tendency along the northern wall in the meander sector located upstream from the trough. This provides a basis for understanding why submesoscale instabilities and cross-wall intrusion and streamer events are more prevalent along the sector downstream from the trough and at the crest where there is not such a frontogenetic tendency. An important attribute for this frontogenesis pattern is the 3D shape of the jet, whose idealization is summarized above.

Description: 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.

Description: The formation and evolution of a diffusive interface in a stable salt-stratified layer cooled from above is studied in a two-dimensional geometry by direct numerical simulation. For a typical example with realistic parameters, the evolution of the flow is computed up to the moment where three layers can be distinguished. Focus is on the development of the first mixed layer. The convective velocity scaling as proposed by Hunt (1984) and previously proposed expressions for the interfacial heat flux (Huppert 1971; Fernando 1989a) are shown to correspond well with the results of the simulation. The evolution of the first layer can be well described by an entrainment relation based on a local balance between kinetic and potential energy with mixing efficiency γ. The new entrainment relation is shown to fit the numerical results well and an interpretation of γ in terms of the overall energy balances of the flow is given. Previously, two rival mechanisms have been proposed that determine the final thickness of the first layer (Turner 1968; Fernando 1987). One of the distinguishing itures of both mechanisms is whether a transition in entrainment regime - as the first layer develops - is a necessary condition for the mixed layer to stop growing. Another the presence of a buoyancy jump over the interface before substantial convection the second layer occurs. From the numerical results, we find a significant buoyancy jump even before the thermal boundary layer ahead of the first layer becomes unstable. Moreover, the convective activity in the second layer is too small to be able to stop the growth of the first layer. We therefore favour the view proposed by Fernando (1987) that a transition in entrainment regime determines the thickness of the first layer. Following this, a new one-dimensional model of layer formation is proposed. Important expressions within this model are verified using the results of the numerical simulation. The model contains two constants which are determined from the numerical results. The results of the new model fit experimental results quite well and the parameter dependence of the thickness of the first layer is not sensitive to the values of the two constants.

Description: The bifurcation structure of thermohaline-driven flows is studied within one of the simplest zonally averaged models which captures thermohaline transport: a Boussinesq model of surface-forced thermohaline flow in a two-dimensional rectangular basin. Under mixed boundary conditions, i.e. prescribed surface temperature and fresh-water flux, it is shown that symmetry breaking originates from a codimension-two singularity which arises through the intersection of the paths of two symmetry-breaking pitchfork bifurcations. The physical mechanism of symmetry breaking of both the thermally and salinity dominated symmetric solution is described in detail from the perturbation structures near bifurcation. Limit cycles with an oscillation period in the order of the overturning time scale arise through Hopf bifurcations on the branches of asymmetric steady solutions. The physical mechanism of oscillation is described in terms of the most unstable mode just at the Hopf bifurcation. The occurrence of these oscillations is quite sensitive to the shape of the prescribed fresh-water flux. Symmetry breaking still occurs when, instead of a fixed temperature, a Newtonian cooling condition is prescribed at the surface. There is only quantitative sensitivity, i.e. the positions of the bifurcation points shift with the surface heat transfer coefficient. There are no qualitative changes in the bifurcation diagram except in the limit where both the surface heat flux and fresh-water flux are prescribed. The bifurcation structure at large aspect ratio is shown to converge to that obtained by asymptotic theory. The complete structure of symmetric and asymmetric multiple equilibria is shown to originate from a codimension-three bifurcation, which arises through the intersection of a cusp and the codimension-two singularity responsible for symmetry breaking.

Description: The California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

Description: The stability is investigated of the swirling flow between two concentric cylinders in the presence of stable axial linear density stratification, for flows not satisfying the well-known Rayleigh criterion for inviscid centrifugal instability, d(Vr)2/dr 〈 0. We show by a linear stability analysis that a sufficient condition for non-axisymmetric instability is, in fact, d(V/r)2/dr 〈 0, which implies a far wider range of instability than previously identified. The most unstable modes are radially smooth and occur for a narrow range of vertical wavenumbers. The growth rate is nearly independent of the stratification when the latter is strong, but it is proportional to it when it is weak, implying stability for an unstratified flow. The instability depends strongly on a non-dimensional parameter, S, which represents the ratio between the strain rate and twice the angular velocity of the flow. The instabilities occur for anti-cyclonic flow (S 〈 0). The optimal growth rate of the fastest-growing mode, which is non-oscillatory in time, decays exponentially fast as S (which can also be considered a Rossby number) tends to 0. The mechanism of the instability is an arrest and phase-locking of Kelvin waves along the boundaries by the mean shear flow. Additionally, we identify a family of (probably infinitely many) unstable modes with more oscillatory radial structure and slower growth rates than the primary instability. We determine numerically that the instabilities persist for finite viscosity, and the unstable modes remain similar to the inviscid modes outside boundary layers along the cylinder walls. Furthermore, the nonlinear dynamics of the anti-cyclonic flow are dominated by the linear instability for a substantial range of Reynolds numbers.

Description: The oceanic general circulation is forced at large scales and is unstable to mesoscale eddies. Large-scale currents and eddy flows are approximately in geostrophic balance. Geostrophic dynamics is characterized by an inverse energy cascade except for dissipation near the boundaries. In this paper, we confront the dilemma of how the general circulation may achieve dynamical equilibrium in the presence of continuous large-scale forcing and the absence of boundary dissipation. We do this with a forced horizontal flow with spatially uniform rotation, vertical stratification and vertical shear in a horizontally periodic domain, i.e. a version of Eady's flow carried to turbulent equilibrium. A direct route to interior dissipation is presented that is essentially non-geostrophic in its dynamics, with significant submesoscale frontogenesis, frontal instability and breakdown, and forward kinetic energy cascade to dissipation. To support this conclusion, a series of simulations is made with both quasigeostrophic and Boussinesq models. The quasigeostrophic model is shown as increasingly inefficient in achieving equilibration through viscous dissipation at increasingly higher numerical resolution (hence Reynolds number), whereas the non-geostrophic Boussinesq model equilibrates with only weak dependence on resolution and Rossby number. © 2010 Cambridge University Press.

Description: Gravitational available potential energy is a central concept in an energy analysis of flows in which buoyancy effects are dynamically important. These include, but are not limited to, most geophysical flows with persistently stable density stratification. The volume-integrated available potential energy ap is defined as the difference between the gravitational potential energy of the system and the potential energy of a reference state with the lowest potential energy that can be reached by adiabatic material rearrangement; ap determines how much energy is available for conservative dynamical exchange with kinetic energy k. In this paper we introduce new techniques for computing the local available potential energy density Eap in numerical simulations that allow for a more accurate and complete analysis of the available potential energy and its dynamical balances as part of the complete energy cycle of a flow. In particular, the definition of Eap and an associated gravitation disturbance field permit us to make a spectral decomposition of its dynamical balance and examine the cross-scale energy flux. Several examples illustrate the spatial structure of Eap and its evolutionary influences. The greatest attention is given to an analysis of a turbulent-equilibrium simulation Eady-like vertical-shear flow with rotation and stable stratification. In this regime Eap exhibits a vigorous forward energy cascade from the mesoscale through the submesoscale range-first in a scale range dominated by frontogenesis and positive buoyancy-flux conversion from ap to k and then, after strong frontal instability and frontogenetic arrest, in a coupled kinetic-potential energy inertial-cascade range with negative buoyancy-flux conversion-en route to fine-scale dissipation of both energy components. Copyright © Cambridge University Press 2010.