Ross Tulloch

A theory for the atmospheric energy spectrum: depth-limited temperature anomalies at the tropopause.

The horizontal spectra of atmospheric wind and temperature at the tropopause have a steep −3 slope at synoptic scales, but transition to −5/3 at wavelengths of the order of 500–1,000 km [Nastrom, G. D. & Gage, K. S. (1985) J. Atmos. Sci. 42, 950–960]. Here we demonstrate that a model that assumes zero potential vorticity and constant stratification N over a finite-depth H in the troposphere exhibits the same type of spectra. In this model, temperature perturbations generated at the planetary scale excite a direct cascade of energy with a slope of −3 at large scales, −5/3 at small scales, and a transition near horizontal wavenumber kt = f/NH, where f is the Coriolis parameter. Ballpark atmospheric estimates for N, f, and H give a transition wavenumber near that observed, and numerical simulations of the previously undescribed model verify the expected behavior. Despite its simplicity, the model is consistent with a number of perplexing features in the observations and demonstrates that a complete theory for mesoscale dynamics must take temperature advection at boundaries into account.

Quasigeostrophic Turbulence with Explicit Surface Dynamics: Application to the Atmospheric Energy Spectrum

Abstract The horizontal wavenumber spectra of wind and temperature near the tropopause have a steep −3 slope at synoptic scales and a shallower −5/3 slope at mesoscales, with a transition between the two regimes at a wavelength of about 450 km. Here it is demonstrated that a quasigeostrophic model driven by baroclinic instability exhibits such a transition near its upper boundary (analogous to the tropopause) when surface temperature advection at that boundary is properly resolved and forced. To accurately represent surface advection at the upper and lower boundaries, the vertical structure of the model streamfunction is decomposed into four parts, representing the interior flow with the first two neutral modes, and each surface with its Green’s function solution, resulting in a system with four prognostic equations. Mean temperature gradients are applied at each surface, and a mean potential vorticity gradient consisting both of β and vertical shear is applied in the interior. The system exhibits three f...

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...

Exploring Mechanisms of Variability and Predictability of Atlantic Meridional Overturning Circulation in Two Coupled Climate Models

AbstractMultidecadal variability in the Atlantic meridional overturning circulation (AMOC) of the ocean is diagnosed in the NCAR Community Climate System Model, version 3 (CCSM3), and the GFDL Coupled Model (CM2.1). Common diagnostic approaches are applied to draw out similarities and differences between the two models. An index of AMOC variability is defined, and the manner in which key variables covary with it is determined. In both models the following is found. (i) AMOC variability is associated with upper-ocean (top 1 km) density anomalies (dominated by temperature) on the western margin of the basin in the region of the Mann eddy with a period of about 20 years. These anomalies modulate the trajectory and strength of the North Atlantic Current. The importance of the western margin is a direct consequence of the thermal wind relation and is independent of the mechanisms that create those density anomalies. (ii) Density anomalies in this key region are part of a larger-scale pattern that propagates ar...

Float-Derived Isopycnal Diffusivities in the DIMES Experiment

As part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), 210 subsurface floats were deployed west of the Drake Passage on two targeted density surfaces. Absolute (single particle) diffusivities are calculated for the floats. The focus is on the meridional component, which is less affectedby the meanshear.The diffusivitiesare estimatedin severalways, including a novelmethodbased on the probability density function of the meridional displacements. This allows the determination of the range of possible lateral diffusivities, as well as the period over which the spreading can be said to be diffusive. The method is applied to the float data and to synthetic trajectories generated with the Massachusetts Institute of TechnologyGeneral CirculationModel (MITgcm).Becauseof ballastingproblems, manyofthefloatsdid not remain on their targeted density surface. However, the float temperature records suggest that most occupied asmallrangeofdensities,sothefloatsweregroupedtogetherfortheanalysis.Thelatterfocuseson asubsetof 109 of the floats, launched near 1058W. The different methods yield a consistent estimate for the diffusivity of 800 6 200m 2 s 21 . The same calculations were made with model particles deployed on 20 different density surfaces and the result for the particles deployed on the neutral density surface g 5 27.7 surface was the same within the errors. The model was then used to map the variation of the diffusivity in the vertical, near the core of the Antarctic Circumpolar Current (ACC). The results suggest mixing is intensified at middepths, between 1500 and 2000m, consistent with several previous studies.

Rationalizing the Spatial Distribution of Mesoscale Eddy Diffusivity in Terms of Mixing Length Theory

Observations and theory suggest that lateral mixing by mesoscale ocean eddies only reaches its maximum potential at steering levels, surfaces at which the propagation speed of eddies approaches that of the mean flow. Away from steering levels, mixing is strongly suppressed because the mixing length is smaller than the eddy scale, thus reducing the mixing rates. The suppression is particularly pronounced in strong currents where mesoscale eddies are most energetic. Here, a framework for parameterizing eddy mixing is explored that attempts to capture this suppression. An expression of the surface eddy diffusivity proposed by Ferrari and Nikurashin is evaluated using observations of eddy kinetic energy, eddy scale, and eddy propagation speed. The resulting global maps of eddy diffusivity have a broad correspondence with recent estimates of diffusivity based on the rate at which tracer contours are stretched by altimetric-derived surface currents. Finally, the expression for the eddy diffusivity is extrapolated in the vertical to infer the eddy-induced meridional heat transport and the overturning streamfunction.

On the Relationship between Decadal Buoyancy Anomalies and Variability of the Atlantic Meridional Overturning Circulation

AbstractOwing to the role of the Atlantic meridional overturning circulation (AMOC) in ocean heat transport, AMOC variability is thought to play a role in climate variability on a wide range of time scales. This paper focuses on the potential role of the AMOC in climate variability on decadal time scales. Coupled and ocean-only general circulation models run in idealized geometries are utilized to study the relationships between decadal AMOC and buoyancy variability and determine whether the AMOC plays an active role in setting sea surface temperature on decadal time scales. Decadal AMOC variability is related to changes in the buoyancy field along the western boundary according to the thermal wind relation. Buoyancy anomalies originate in the upper ocean of the subpolar gyre and travel westward as baroclinic Rossby waves. When the buoyancy anomalies strike the western boundary, they are advected southward by the deep western boundary current, leading to latitudinally coherent AMOC variability. The AMOC i...

A note on the numerical representation of surface dynamics in quasigeostrophic turbulence: Application to the nonlinear eady model

Abstract The quasigeostrophic equations consist of the advection of linearized potential vorticity coupled with advection of temperature at the bounding upper and lower surfaces. Numerical models of quasigeostrophic flow often employ greater (scaled) resolution in the horizontal than in the vertical (the two-layer model is an extreme example). In the interior, this has the effect of suppressing interactions between layers at horizontal scales that are small compared to Nδz/f (where δz is the vertical resolution, N the buoyancy frequency, and f the Coriolis parameter). The nature of the turbulent cascade in the interior is, however, not fundamentally altered because the downscale cascade of potential enstrophy in quasigeostrophic turbulence and the downscale cascade of enstrophy in two-dimensional turbulence (occurring layerwise) both yield energy spectra with slopes of −3. It is shown here that a similar restriction on the vertical resolution applies to the representation of horizontal motions at the surf...

The Global Characteristics of the Wavenumber Spectrum of Ocean Surface Wind

The wavenumber spectra of wind kinetic energy over the ocean from Quick Scatterometer (QuikSCAT) observations have revealed complex spatial variability in the wavelength range of 1000‐3000 km, with spectral slopes varying from 21.6 to 22.9. Here the authors performed a spectral analysis of QuikSCAT winds over the global ocean and found that (i) the spectral slopes become steeper toward the Poles in the Pacificandin the South Atlantic,and theslopes exhibitminimallongitudinaldependencein the SouthPacific; (ii) thesteepestslopesare inthe tropical IndianOcean andthe shallowest slopesarein thetropicalPacificand Atlantic; and (iii) the spectra are steeper in winter than summer in most regions of the midlatitude Northern Hemisphere.Thenewfindingsreportedinthepaperprovideatestbedfortheoreticalstudiesandatmospheric general circulation models.