Christopher L. Wolfe

What Sets the Strength of the Middepth Stratification and Overturning Circulation in Eddying Ocean Models

Abstract The processes maintaining stratification in the oceanic middepth (between approximately 1000 and 3000 m) are explored using an eddy-resolving general circulation model composed of a two-hemisphere, semienclosed basin with a zonal reentrant channel in the southernmost eighth of the domain. The middepth region lies below the wind-driven main thermocline but above the diffusively driven abyssal ocean. Here, it is argued that middepth stratification is determined primarily in the model’s Antarctic Circumpolar Current. Competition between mean and eddy overturning in the channel leads to steeper isotherms and thus deeper stratification throughout the basin than would exist without the channel. Isotherms that outcrop only in the channel are nearly horizontal in the semienclosed portion of the domain, whereas isotherms that also outcrop in the Northern Hemisphere deviate from horizontal and are accompanied by geostrophically balanced meridional transport. A northern source of deep water (water with temp...

The Adiabatic Pole-to-Pole Overturning Circulation

AbstractThe adiabatic pole-to-pole cell of the residual overturning circulation (ROC) is studied in a two-hemisphere, semienclosed basin, with a zonally reentrant channel occupying the southernmost eighth of the domain. Three different models of increasing complexity are used: a simple, analytically tractable zonally averaged model; a coarse-resolution numerical model with parameterized eddies; and an eddy-resolving general circulation model. Two elements are found to be necessary for the existence of an adiabatic pole-to-pole cell: 1) a thermally indirect, wind-driven overturning circulation in the zonally reentrant channel, analogous to the Deacon cell in the Antarctic Circumpolar Current (ACC) region, and 2) a set of outcropping isopycnals shared between the channel and the semienclosed region of the Northern Hemisphere. These points are supported by several computations varying the domain geometry, the surface buoyancy distribution, and the wind forcing. All three models give results that are qualitat...

Laboratory Experiments on Eddy Generation by a Buoyant Coastal Current Flowing over Variable Bathymetry

Irminger rings are warm-core eddies formed off the west coast of Greenland. Recent studies suggest that these eddies, which are implicated in the rapid springtime restratification of the Labrador Sea, are formed by an internal instability of the West Greenland Current (WGC), triggered by bathymetric variations. This study seeks to explore the effect of the magnitude and downstream length scale of bathymetric variations on the stability of a simple model of the WGC in a series of laboratory experiments in which a buoyant coastal current was allowed to flow over bathymetry consisting of piecewise constant slopes of varying magnitude. The currents did not form eddies over gently sloping bathymetry and only formed eddies over steep bathymetry if the current width exceeded the width of the sloping bathymetry. Eddying currents were immediately stabilized if they flowed onto gently sloping topography. Bathymetric variations that persisted only a short distance downstream perturbed the flow locally but did not lead to eddy formation. Eddies formed only once the downstream length of the bathymetric variations exceeded a critical scale of about 8 Rossby radii. These results are consistent with the observed behavior of the WGC, which begins to form Irminger rings after entering a region where the continental slope abruptly steepens and becomes narrower than the WGC itself in a region spanning about 20–80 Rossby radii of downstream distance.

Overturning Circulation in an Eddy-Resolving Model: The Effect of the Pole-to-Pole Temperature Gradient

The effect of the pole-to-pole surface temperature difference on the deep stratification and the strength of the global meridional overturning circulation (MOC) is examined in an eddy-resolving ocean model configured in an idealized domain roughly representing the Atlantic sector. Mesoscale eddies lead to qualitative differences in the mean stratification and the MOC compared to laminar (i.e., eddy free) models. For example, the spreading of fluid across the model’s representation of the Antarctic Circumpolar Current (ACC) no longer relies on the existence of a sill in the ACC. In addition, the deep- and bottom-water masses— roughly representing North Atlantic Deep Water (NADW) and Antarctic Bottom Water (ABW), respectively—are eroded by the eddies so that their zonal and meridional extents are much smaller than in the laminar case. It is found that if the north pole temperature is sufficiently warm, the formation of northern deep water is suppressed and the middepth cell is small and weak while the deep cell is large and vigorous. In contrast, if the north pole temperatureis in the range of the southern channeltemperatures,the middepth cell is large andstrong while the deep cell has a reducedamplitude.This result is consistentwith the predictionsof the laminar theory of the MOC. In contrast to the laminar theory, realistically strong deep stratification is formed even if the temperature at the northern sinking site is warmer than any temperature found in the channel. Indeed, middepth stratification is actually stronger in the latter case than the former case.

Eddy-Driven Buoyancy Gradients on Eastern Boundaries and Their Role in the Thermocline

Abstract It is demonstrated that eddy fluxes of buoyancy at the eastern and western boundaries maintain alongshore buoyancy gradients along the coast. Eddy fluxes arise near the eastern and western boundaries because on both coasts buoyancy gradients normal to the boundary are strong. The eddy fluxes are accompanied by mean vertical flows that take place in narrow boundary layers next to the coast where the geostrophic constraint is broken. These ageostrophic cells have a velocity component normal to the coast that balances the geostrophic mean velocity. It is shown that the dynamics in these thin ageostrophic boundary layers can be replaced by effective boundary conditions for the interior flow, relating the eddy flux of buoyancy at the seaward edge of the boundary layers to the buoyancy gradient along the coast. These effective boundary conditions are applied to a model of the thermocline linearized around a mean stratification and a state of rest. The linear model parameterizes the eddy fluxes of buoya...

Salt Feedback in the Adiabatic Overturning Circulation

The adiabatic overturning circulation is the part of the meridional overturning circulation that persists in the limit of vanishing diffusivity. Two conditions are required for the existence of the adiabatic overturning circulation: a high-latitude zonally reentrant channel subject to surface westerlies and a set of outcropping isopycnals shared between the channel and the opposite hemisphere. This paper examines how different buoyancy forcing regimes, particularly freshwater flux, affect the surface buoyancy distribution and the strengthoftheadiabaticoverturningcirculation.Withoutfreshwaterforcing,salinityisuniformandbuoyancy is determined by temperature only. In this case, the size of the shared isopycnal window is effectively fixed by thecouplingbetweenatmosphericandseasurfacetemperatures.Withfreshwaterforcing(appliedasasurface flux), the salinity, and thus the sea surface buoyancy and the size of the shared isopycnal window, is not specified by the atmospheric state alone. It is found that a salt‐advection feedback leads to surface buoyancy distributions that increase the size of the isopycnal window and strengthen the adiabatic overturning circulation. The strength of the feedback is controlled by processes in high latitudes—the southern channel, where the surface salinity is determined by a balancebetween freshwater input from the atmosphere, salt input from upwelling deep water, and freshwater export by Ekman transport; and the Northern Hemisphere, where the overturning and wind-driven transport in the thermocline advect salty water from the subtropics, mitigating the freshening effect of the surface freshwater flux. The freshwater budget in the channel region provides an estimate of the size of the isopycnal window.

Eastern-Boundary Contribution to the Residual and Meridional Overturning Circulations

A model of the thermocline linearized around a specified stratification and the barotropic linear winddriven Stommel solution is constructed. The forcings are both mechanical (the surface wind stress) and thermodynamical (the surface buoyancy boundarycondition). The effects of diapycnal diffusivity and of eddy fluxesofbuoyancy,parameterizedintermsofthelarge-scalebuoyancygradient,areincluded.Theeddyfluxes of buoyancy are especially important near the boundaries where they mediate the transport in and out of the narrow ageostrophic down-/upwelling layers. The dynamics of these narrow layers can be replaced by effective boundary conditions on the geostrophically balanced flow. The effective boundary conditions state that the residual flow normal to the effective coast vanishes. The separate Eulerian and eddy-induced components may be nonzero. This formulation conserves the total mass and the total buoyancy while permitting an exchangebetweentheEulerianandeddytransportofbuoyancy withinthedown-/upwellinglayers.Inturn, this exchange allows buoyancy gradients along all solid boundaries, including the eastern one. A special focus is on the buoyancy along the eastern and western walls since east‐west buoyancy difference determines the meridional overturning circulation. The inclusion of advection of buoyancy by the barotropic flow allows a meaningful distinction between the meridional and the residual overturning circulations while retaining the simplicity of a linear model. The residual flow in both meridional and zonal directions reveals how the subsurface buoyancy distribution is established and, in particular, how the meridional buoyancy gradient is reversed at depth. In turn, the horizontal buoyancy gradient maintains stacked counterrotating cells in the meridional and residual overturning circulations. Quantitative scaling arguments are given for each of these cells, which show how the buoyancy forcing, the wind stress, and the diapycnal and eddy diffusivities, as well as the other imposed parameters, affect the strength of the overturn.

Normal-Mode Analysis of a Baroclinic Wave-Mean Oscillation

The stability of a time-periodic baroclinic wave-mean oscillation in a high-dimensional two-layer quasigeostrophic spectral model is examined by computing a full set of time-dependent normal modes (Floquet vectors) for the oscillation. The model has 72 62 horizontal resolution and there are 8928 Floquet vectors in the complete set. The Floquet vectors fall into two classes that have direct physical interpretations: wave-dynamical (WD) modes and damped-advective (DA) modes. The WD modes (which include two neutral modes related to continuous symmetries of the underlying system) have large scales and can efficiently exchange energy and vorticity with the basic flow; thus, the dynamics of the WD modes reflects the dynamics of the wave-mean oscillation. These modes are analogous to the normal modes of steady parallel flow. On the other hand, the DA modes have fine scales and dynamics that reduce, to first order, to damped advection of the potential vorticity by the basic flow. While individual WD modes have immediate physical interpretations as discrete normal modes, the DA modes are best viewed, in sum, as a generalized solution to the damped advection problem. The asymptotic stability of the time-periodic basic flow is determined by a small number of discrete WD modes and, thus, the number of independent initial disturbances, which may destabilize the basic flow, is likewise small. Comparison of the Floquet exponent spectrum of the wave-mean oscillation to the Lyapunov exponent spectrum of a nearby aperiodic trajectory suggests that this result will still be obtained when the restriction to time periodicity is relaxed.

A Nonlinear Baroclinic Wave-Mean Oscillation with Multiple Normal Mode Instabilities

Abstract An unstable, nonlinear baroclinic wave-mean oscillation is found in a strongly supercritical quasigeostrophic f-plane numerical channel model with 3840 Fourier components. The growth of linear disturbances to this time-periodic oscillation is analyzed by computing time-dependent normal modes (Floquet vectors). Two different Newton–Picard methods are used to compute the unstable solution, the first based on direct computation of a large set of Floquet vectors, and the second based on an efficient iterative solver. Three different growing normal modes are found, which modify the wave structure of the wave-mean oscillation in two essentially different ways. The dynamics of the instabilities are qualitatively similar to the baroclinic dynamics of the wave-mean oscillation. The results provide an example of time-dependent normal mode instability of a strongly nonlinear time-dependent baroclinic flow.

Singular Vectors and Time-Dependent Normal Modes of a Baroclinic Wave-Mean Oscillation

Abstract Linear disturbance growth is studied in a quasigeostrophic baroclinic channel model with several thousand degrees of freedom. Disturbances to an unstable, nonlinear wave-mean oscillation are analyzed, allowing the comparison of singular vectors and time-dependent normal modes (Floquet vectors). Singular vectors characterize the transient growth of linear disturbances in a specified inner product over a specified time interval and, as such, they complement and are related to Lyapunov vectors, which characterize the asymptotic growth of linear disturbances. The relationship between singular vectors and Floquet vectors (the analog of Lyapunov vectors for time-periodic systems) is analyzed in the context of a nonlinear baroclinic wave-mean oscillation. It is found that the singular vectors divide into two dynamical classes that are related to those of the Floquet vectors. Singular vectors in the “wave dynamical” class are found to asymptotically approach constant linear combinations of Floquet vector...