Geoffrey K. Vallis

Generation of mean flows and jets on a beta plane and over topography

Abstract This paper proposes and discusses mechanisms whereby mean flows and jets are produced by differential rotation and by topographic effects. It is shown that, in general, a mean gradient of potential vorticity not only inhibits the cascade of energy to large scales but directly produces anisotropic structures. Scalings for this are examined on the β plane using ideas from classical phenomenology. The scalings are naturally anisotropic and predict the formation of zonal flows directly through a turbulent cascade. Numerical simulations and two-point closure calculations qualitatively confirm the predictions. Also, simulations of barotropic flow on the β plane can produce zonal jet structures of exceptional persistence over many eddy turnover times. Unsteady flow over topography generally produces a mean flow with a correlation between streamfunction and topography, with anticyclonic motion over humps. If the topography is shallow (or the flow sufficiently energetic) the mean streamfunction will be of...

Probing the Fast and Slow Components of Global Warming by Returning Abruptly to Preindustrial Forcing

Abstract The fast and slow components of global warming in a comprehensive climate model are isolated by examining the response to an instantaneous return to preindustrial forcing. The response is characterized by an initial fast exponential decay with an e-folding time smaller than 5 yr, leaving behind a remnant that evolves more slowly. The slow component is estimated to be small at present, as measured by the global mean near-surface air temperature, and, in the model examined, grows to 0.4°C by 2100 in the A1B scenario from the Special Report on Emissions Scenarios (SRES), and then to 1.4°C by 2300 if one holds radiative forcing fixed after 2100. The dominance of the fast component at present is supported by examining the response to an instantaneous doubling of CO2 and by the excellent fit to the model’s ensemble mean twentieth-century evolution with a simple one-box model with no long times scales.

Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence

Results from a wide range of direct numerical simulations of forced-dissipative, differentially rotating two-dimensional turbulence are presented, in order to delineate the broad dependence of flow type on forcing parameters. For most parameter values the energy spectra of simulations forced at low wavenumbers are markedly steeper than the classical k −3 enstrophy inertial-range prediction, and although k −3 spectra can be produced under certain circumstances, the regime is not robust, and the Kolmogorov constant is not universal unless a slight generalization is made in the phenomenology. Long-lived, coherent vortices form in many cases, accompanied by steep energy spectra and a higher than Gaussian vorticity kurtosis. With the addition of differential rotation (the β-effect), a small number of fairly distinct flow regimes are observed. Coherent vortices weaken and finally disappear as the strength of the β-effect increases, concurrent with increased anisotropy and decreased kurtosis. Even in the absence of coherent vortices and with a Gaussian value of the kurtosis, the spectra remain relatively steep, although not usually as steep as for the non-rotating cases. If anisotropy is introduced at low wavenumbers, the anisotropy is transferred to all wavenumbers in the inertial range, where the dynamics are isotropic. For those simulations that are forced at relatively high wavenumbers, a well resolved and very robust k −5/3 energy inertial range is observed, and the Kolmogorov constant appears universal. The low-wavenumber extent of the reverse energy cascade is essentially limited by the β-effect, which produces an effective barrier in wavenumber space at which energy accumulates, and by frictional effects which must be introduced to achieve equilibrium. Anisotropy introduced at large scales remains largely confined to the low wavenumbers, rather than being cascaded to small scales. When there is forcing at both large and small scales (which is of relevance to the Earths atmosphere), energy and enstrophy inertial ranges coexist, with an upscale energy transfer and downscale enstrophy transfer in the same wavenumber interval, without the need for any dissipation mechanism between forcing scales.

A Mechanism and Simple Dynamical Model of the North Atlantic Oscillation and Annular Modes

A simple dynamical model is presented for the basic spatial and temporal structure of the large-scale modes of intraseasonal variability and associated variations in the zonal index. Such variability in the extratropical atmosphere is known to be represented by fairly well-defined patterns, and among the most prominent are the North Atlantic Oscillation (NAO) and a more zonally symmetric pattern known as an annular mode, which is most pronounced in the Southern Hemisphere. These patterns may be produced by the momentum fluxes associated with large-scale midlatitude stirring, such as that provided by baroclinic eddies. It is shown how such stirring, as represented by a simple stochastic forcing in a barotropic model, leads to a variability in the zonal flow via a variability in the eddy momentum flux convergence and to patterns similar to those observed. Typically, the leading modes of variability may be characterized as a mixture of ‘‘wobbles’’ in the zonal jet position and ‘‘pulses’’ in the zonal jet strength. If the stochastic forcing is statistically zonally uniform, then the resulting patterns of variability as represented by empirical orthogonal functions are almost zonally uniform and the pressure pattern is dipolar in the meridional direction, resembling an annular mode. If the forcing is enhanced in a zonally localized region, thus mimicking the effects of a storm track over the ocean, then the resulting variability pattern is zonally localized, resembling the North Atlantic Oscillation. This suggests that the North Atlantic Oscillation and annular modes are produced by the same mechanism and are manifestations of the same phenomenon. The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by the equations of motion limited by the effects of nonlinear dynamics and friction. For reasonable parameters these produce a decorrelation time of the order of 5‐10 days. The model also produces some long-term (100 days or longer) variability, without imposing such variability via the external parameters except insofar as it is contained in the nearly white stochastic forcing.

Turbulent diffusion in the geostrophic inverse cascade

Motivated in part by the problem of large-scale lateral turbulent heat transport in the Earths atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed two-dimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical two-dimensional turbulence, surface quasi-geostrophic turbulence, and shallow-water quasi-geostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a large-scale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes. When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When β is significant, we find a clear distinction between the tracer mixing scale, which depends on β but is nearly independent of drag, and the energy-containing (or jet) scale, set by a combination of the drag coefficient and β. Our predictions are tested via high- resolution spectral simulations. We find in all cases that the passive scalar is diffused down-gradient with a diffusion coefficient that is well-predicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.

Large-scale circulation with small diapycnal diffusion: The two-thermocline limit

The structure and dynamics of the large-scale circulation of a single-hemisphere, closed-basin ocean with small diapycnal diffusion are studied by numerical and analytical methods. The investigation is motivated in part by recent differing theoretical descriptions of the dynamics that control the stratification of the upper ocean, and in part by recent observational evidence that diapycnal diffusivities due to small-scale turbulence in the ocean thermocline are small (-0.1 cm2 s-i). Numerical solutions of a computationally efficient, three-dimensional, planetary geostrophic ocean circulation model are obtained in a square basin on a mid-latitude B-plane. The forcing consists of a zonal wind stress (imposed meridional Ekman flow) and a surface heat llux proportional to the difference between surface temperature and an imposed air temperature. For small diapycnal diffusivities (vertical:

Eddy–Zonal Flow Interactions and the Persistence of the Zonal Index

Abstract An idealized atmospheric general circulation model is used to investigate the factors controlling the time scale of intraseasonal (10–100 day) variability of the extratropical atmosphere. Persistence on these time scales is found in patterns of variability that characterize meridional vacillations of the extratropical jet. Depending on the degree of asymmetry in the model forcing, patterns take on similar properties to the zonal index, annular modes, and North Atlantic Oscillation. It is found that the time scale of jet meandering is distinct from the obvious internal model time scales, suggesting that interaction between synoptic eddies and the large-scale flow establish a separate, intraseasonal time scale. A mechanism is presented by which eddy heat and momentum transport couple to retard motion of the jet, slowing its meridional variation and thereby extending the persistence of zonal index and annular mode anomalies. The feedback is strong and quite sensitive to model parameters when the mod...

Large-Scale Circulation and Production of Stratification: Effects of Wind, Geometry, and Diffusion

The combined effects of wind, geometry, and diffusion on the stratification and circulation of the ocean are explored by numerical and analytical methods. In particular, the production of deep stratification in a simply configured numerical model with small diffusivity is explored. In the ventilated thermocline of the subtropical gyre, the meridional temperature gradient is mapped continously to a corresponding vertical profile, essentially independently of (sufficiently small) diffusivity. Below this, as the vertical diffusivity tends to zero, the mapping becomes discontinuous and is concentrated in thin diffusive layers or internal thermoclines. It is shown that the way in which the thickness of the main internal thermocline (i.e., the diffusive lower part of the main thermocline), and the meridional overturning circulation, scales with diffusivity differs according to the presence or absence of a wind stress. For realistic parameter values, the ocean is in a scaling regime in which wind effects are important factors in the scaling of the thermohaline circulation, even for the single hemisphere, flat-bottomed case. It is shown that deep stratification may readily be produced by the combined effects of surface thermodynamic forcing and geometry. The form of the stratification, but not its existence, depends on the diffusivity. Such deep stratification is efficiently produced, even in single-basin, single-hemisphere simulations, in the presence of a partially topographically blocked channel at high latitudes, provided there is also a surface meridional temperature gradient across the channel. For sufficiently simple geometry and topography, the abyssal stratification is a maximum at the height of the topography. In the limit of small diffusivity, the stratification becomes concentrated in a thin diffusive layer, or front, whose thickness appears to scale as the one-third power of the diffusivity. Above and below this diffusive abyssal thermocline are thick, largely adiabatic and homogeneous water masses. In two hemisphere integrations, the water above the abyssal thermocline may be either ‘‘intermediate’’ water from the same hemisphere as the channel, or ‘‘deep’’ water from the opposing hemisphere, depending on whether the densest water from the opposing hemisphere is denser than the surface water at the equatorward edge of the channel. The zonal velocity in the channel is in thermal wind balance, thus determined more by the meridional temperature gradient across the channel than by the wind forcing. If the periodic channel extends equatorward past the latitude of zero wind-stress curl, the poleward extent of the ventilated thermocline, and the surface source of the mode water, both then lie at the equatorial boundary of the periodic circumpolar channel, rather than where the wind stress curl changes sign.

Routes to energy dissipation for geostrophic flows in the Southern Ocean

Wind power inputs at the surface ocean are dissipated through smaller-scale processes in the ocean interior and turbulent boundary layer. Simulations suggest that seafloor topography enhances turbulent mixing and energy dissipation in the ocean interior. The ocean circulation is forced at a global scale by winds and fluxes of heat and fresh water. Kinetic energy is dissipated at much smaller scales in the turbulent boundary layers and in the ocean interior1,2, where turbulent mixing controls the transport and storage of tracers such as heat and carbon dioxide3,4. The primary site of wind power input is the Southern Ocean, where the westerly winds are aligned with the Antarctic Circumpolar Current5. The potential energy created here is converted into a vigorous geostrophic eddy field through baroclinic instabilities. The eddy energy can power mixing in the ocean interior6,7,8, but the mechanisms governing energy transfer to the dissipation scale are poorly constrained. Here we present simulations that simultaneously resolve meso- and submeso-scale motions as well as internal waves generated by topography in the Southern Ocean. In our simulations, more than 80% of the wind power input is converted from geostrophic eddies to smaller-scale motions in the abyssal ocean. The conversion is catalysed by rough, small-scale topography. The bulk of the energy is dissipated within the bottom 100 m of the ocean, but about 20% is radiated and dissipated away from topography in the ocean interior, where it can sustain turbulent mixing. We conclude that in the absence of rough topography, the turbulent mixing in the ocean interior would be diminished.

Tectonic processes in Papua New Guinea and past productivity in the eastern equatorial Pacific Ocean

Phytoplankton growth in the eastern equatorial Pacific Ocean today accounts for about half of the ‘new’ production—the fraction of primary production fuelled by externally supplied nutrients—in the global ocean. The recent demonstration that an inadequate supply of iron limits primary production in this region supports earlier speculation that, in the past, fluctuations in the atmospheric deposition of iron-bearing dust may have driven large changes in productivity. But we argue here that only small (∼2 nM) increases in the iron concentration in source waters of the upwelling Equatorial Undercurrent are needed to fuel intense diatom production across the entire eastern equatorial Pacific Ocean. Episodic increases in iron concentrations of this magnitude or larger were probably frequent in the past because a large component of the undercurrent originates in the convergent island-arc region of Papua New Guinea, which has experienced intensive volcanic, erosional and seismic activity over the past 16 million years. Cycles of plankton productivity recorded in eastern equatorial Pacific sediments may therefore reflect the influence of tectonic processes in the Papua New Guinea region superimposed on the effects of global climate forcing.