Cambridge University Press, by G. K. Vallis.

Graduate level textbook with a few monograph-like aspects. Contains material on fundamentals of GFD; waves, instabilities and turbulence; general circulation of atmosphere; general circulation of ocean.

Click here for book web site

Princeton University Press, by G. K. Vallis.

A short undergraduate-level that appeared in 2011. It may also be useful as an overview for graduate students and scientists in other fields.

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This is a discussion paper concerned with the response of the large-scale structure of the atmosphere to increased concentrations of greenhouse gases. We present results from CMIP5 integrations as well as reviewing various arguments for how the atmosphere might change, and we discuss what is robust and what is not. Topics include the height of the tropopause, the expansion of the Hadley Cell and the shift of the westerlies. Comments by email to me at my Exeter email address (g.vallis at exeter etc) are welcome.

Potter, S., Vallis, G. K. and Mitchell, J. L. 2013. Spontaneous superrotation and the role of Kelvin waves in an idealized dry GCM

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The nondimensional parameter space of an idealized dry primitive equations model is explored to find superrotating climate states. The model has no convective parameterization and is forced using a simple thermal relaxation to a prescribed radiative equilibrium temperature. It is demonstrated that of four nondimensional parameters that determine the model’s state only the thermal Rossby number has a significant effect on superrotation. The mode that drives the transition to superrotation in an intermediate thermal Rossby number atmosphere is shown to behave like a Kelvin wave in the tropics.

Zhang, Y and Vallis, G. K. 2013. Ocean Heat Uptake in Eddying and Non-eddying Ocean Circulation Models in a Warming Climate

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Ocean heat uptake is explored with non-eddying, eddy-permitting and eddy-resolving (0.125$\dg$) ocean circulation models in an idealized domain crudely representing the Atlantic basin connected to a southern circumpolar channel. Two distinct processes are found relevant for the ensuing heat uptake: heat uptake into the ventilated thermocline forced by Ekman pumping and heat absorption in the deep ocean through meridional overturning circulation (MOC). Temperature increases in the thermocline occur on the decadal timescale whereas, over most of the abyss, it is the millennial time scale that is relevant, and the strength of MOC in the channel matters for the intensity of heat uptake. Under global, uniform warming, the rate of increase of total heat content increases with both diapycnal diffusivity and strengthening southern ocean westerlies.

Farneti, R. and Vallis, G. K. 2013. Meridional Energy Transport in the Coupled Atmosphere-Ocean system: Compensation and Partitioning

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We explore the partitioning of heat transport between the ocean and atmosphere in a hierarchy of models ranging from a coupled GCM to an energy balance model. We find that Bjerknes compensation works in some but not all situations, and works imperfectly. We argue that compensation can best be interpreted as arising from the highly efficient nature of the energy transport in the atmosphere rather than any a priori need for the top-of-atmosphere radiation budget to be fixed.

Jucker, M, Fueglistaler, S, and Vallis, G. K. 2013. Maintenance of stratospheric structure in an idealized general circulation model

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We explore the factors maintaining the structure of the stratosphere, including the tropical cold point, using an idealized general circulation model. We look at the effects of mountain-forced stationary waves, baroclinic waves, and the actual stratospheric thermal forcing. All of these are important in their own way; none may be neglected if some degree of realism is desired.

Zurita-Gotor, P. and Vallis, G. K. 2013. The determination of extratropical tropopause height in an idealized gray-radiation model

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Explores the joint effects of baroclinic turbulence and diabatic forcing in determining the height of the tropopause, using an idealized multi-level primitive equation model with a gray radiation scheme. By and large we find that radiative constraints constrain the tropopause height and prevents an adjustment to marginal criticality. We also find that a mixing barrier forms at the jet maximum when baroclinicity has a finite vertical scale.

O'Rourke, A. and Vallis, G. K., 2013. Jet Interaction and the Influence of a Minimum Phase Speed Bound on the Propagation of Eddies.

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We investigate the interaction between analogs of the subtropical jet and the eddy-driven jet using a barotropic model. Cospectral analysis of eddy momentum flux convergence indicating that eddy activity is generally restricted by both a minimum and maximum phase-speed bound: the wavenumber-dependent minimum phase speed represents a turning line for meridionally propagating waves, and the upper bound representing a critical line. The authors vary the separation distance between the relaxation and stirring regions and find that a sustained, double-jet state is achieved when either a critical or turning latitude forms in the interjet region. The eddy-driven and subtropical jets have a tendency to merge if waves can propagate through the interjet region.

Nikurashin, M, Vallis, G.K. and Adcroft, A. 2013. Routes to energy dissipation for geostrophic flows in the Southern Ocean.

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In an attempt to understand how energy is dissipated in the ocean we performed simulations that simultaneously resolve the mesoscale, submesoscale, and the internal waves generated by topography. Most of the energy is converted from geostrophic eddies to smaller-scale motions in the abyssal ocean, catalyzed by rough, small-scale topography. Although most of the energy is dissipated in the bottom boundary layer, about 20% is radiated into the ocean interior where it becomes the main source of turbulent mixing.

Nikurashin, M. and Vallis, G. K. 2012. A Theory of the Interhemispheric Deep Overturning Circulation and Associated Stratification.

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The paper extends the one listed below to include the mid-depth circulation (i.e., 'NADW'). Thus, we offer a simple theoretic model of the meridional overturning circulation and associated deep stratification in an interhemispheric, single-basin ocean with a circumpolar channel, including the mid-depth circulation (NADW) and the abyssal circulation (AABW). The theory includes the effects of wind, eddies, and diapycnal mixing, and predicts the deep stratification and overturning streamfunction in terms of the surface forcing and other problem parameters. It is a very different model from the traditional Stommel-Arons-Munk type models that rely on mixing. Rather, it tries to quantify and encapsulate recent ideas about the role of the Southern Ocean winds and eddies, and quantify their importance relative to diapycnal mixing.

Ilicak, M. and Vallis, G. K. 2012. Simulations and scaling of horizontal convection.

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We describe some simulations of horizontal convection at Rayleigh numbers of up to 10^11. We explore whether Sandstom's so-called theorem appears to be valid, whether certain scaling relations are satisfied, and what the effects of a stress at the surface are.

Padilla, L., Vallis, G. K. and Rowley, C. 2011. Probabilistic estimates of transient climate sensitivity subject to uncertainty in forcing and natural variability.

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We explore the impact of uncertainty in past forcing and of unforced variability in the climate record on estimates of climate sensitivity. Using a Kalman filter to estimate parameters in an EBM, we provide a range of probabilistic estimates of the transient climate sensitivity (TCS).

Nikurashin, M. and Vallis, G. K. 2011. A Theory of Deep Stratification and Overturning Circulation in the Ocean.

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We offer a simple theoretical model of the deep stratification and meridional overturning circulation in an idealized single-basin ocean with a circumpolar channel. The theory includes the effects of wind, eddies, and diapycnal mixing, predicts the deep stratification in terms of the surface forcing and other problem parameters, makes no assumption of zero residual circulation, and consistently accounts for the interaction between the circumpolar channel and the rest of the ocean (or so it seems to us).

Zurita-Gotor, P. and Vallis, G. K. 2011. Dynamics of mid-latitude tropopause height in an idealized model.

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Explores the joint effects of baroclinic turbulence and diabatic forcing in determining the height of the tropopause, using an idealized multi-level primitive equation model. It is found that when the vertical redistribution of heat is important the radiative constraint tightly constrains the tropopause height and prevents an adjustment to marginal criticality.

Venaille, A, Vallis, G. K. and Smith, K. S. 2011. Baroclinic turbulence in the ocean: analysis with primitive equation and quasi-geostrophic simulations.

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This paper examines the factors determining the distribution, length scale, magnitude and structure of mesoscale oceanic eddies. We find that typically there is a modest transfer of energy (an `inverse cascade') to larger scales in the horizontal, with the length scale of the resulting eddies typically comparable to or somewhat larger than the wavelength of the most unstable mode. The eddies are, however, manifestly nonlinear and in many locations the turbulence is fairly well-developed.

Xie, P. and Vallis, G. K. 2011. The Passive and Active Nature of Ocean Heat Uptake in Idealized Climate Change Experiments

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We explore the extent to which the uptake of heat by the ocean is similar to that of a passive tracer, and to what extent changes in the circulation pattern are important. We find that over a wide range of values of parameters heat uptake is nearly always determined to a greater degree by the existing heat reservoir redistribution than by the nearly passive uptake of temperature due to changes in the surface boundary conditions.

Mitchell, J. and Vallis, G. K. 2010. The transition to superrotation in terrestrial atmospheres

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We explore the transition to superrotation in terrestrial atmospheres (i.e, atmospheres with a solid surface below, such as those on Earth, Mars or Titan). We show that as the thermal Rossby increases, because the planet rotates more slowly or its radius decreases, baroclinic instability in mid-latitudes decreases and barotropic instability increases, and this leads to superrotation.

Kidston, J. and Vallis, G. K. 2010. Relationship between eddy-driven jet latitude and width

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Shows that more poleward jets tend to be wider, in both idealized and comprehensive models, and that barotropic instability might account for this.

Held, I. M, Winton, M., Takahashi, K., Delworth, T., Zeng, F., and Vallis, G. K. 2010. Probing the Fast and Slow Components of Global Warming by Returning Abruptly to Preindustrial Forcing.

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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 years, leaving behind a remnant that evolves more slowly.

Kidston, J., Vallis, G. K., Dean, S.M. and Renwick, J. A. 2011. Can the increase in the eddy length scale under global warming cause the poleward shift of the jet streams?

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This manuscript offers a mechanism whereby an increase in eddy length scales can cause a poleward shift of the eddy-driven jets and surface westerlies, such as is simulated in a large number of comprehensive climate models under global warming.

Kidston, J., Dean, S.M., Renwick, J. A. and Vallis, G. K. 2010. A robust increase in the eddy length scale in the simulation of future climates.

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This paper shows that a large number of comprehensive climate models (in fact all models in CMIP 3) exhibit an increase in the eddy length scale in the future compared with the simulation of 20th Century climate. The increase in length scale is on the order of 5% by the end of the 21st century, and the Southern Hemisphere exhibits a larger increase than the Northern Hemisphere.

Kidston, J., Frierson, D. M. W., Renwick, J. A. and Vallis, G. K. 2010. Observations, Simulations, and Dynamics of Jet Stream Variability and Annular Modes

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The characteristics of the dominant pattern of extra-tropical variability (the so-called annular modes) are examined, and it is shown that there is genuine hemispheric symmetry in the variation of the zonal wind in the Southern Hemisphere but not the Northern Hemisphere, and that the mechanism of the annular mode is baroclinic in origin.

Ferrari, R., Griffies, S. M., Nurser, G. and Vallis, G. K. 2010. A Boundary-Value Problem for the Parameterized Mesoscale Eddy Transport.

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A new method for parameterizing mesoscale eddies in ocean models. The new method, which may be regarded as a variation on the GM scheme, enforces a low mode vertical structure for the parameterized streamfunction, as motivated by geostrophic turbulence theory as for example in the papers by Smith and Vallis below. The scheme also satisfies appropriate boundary conditions at the top and bottom of the ocean without ad hoc tapering.

Zurita-Gotor, P. and Vallis, G. K., 2010. Circulation sensitivity to heating in a simple model of baroclinic turbulence.

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A study of sensitivity of the circulation of an idealized primitive-equation two-level model on the form and strength of the heating, aiming to understand the qualitatively different sensitivity of the isentropic slope (marginally supercritical, highly supercritical, etc) on differential heating reported by previous idealized studies when different model formulations are used. Although motivated in part by the differences that moisture evidently makes, we used a dry model.

Vallis, G. K. and Farneti, R. 2009. Meridional Energy Transport in the Atmosphere-Ocean System. Scaling and Numerical Experiments.

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A discussion of the mechanisms of energy transport in the coupled atmosphere-ocean system, with some scaling estimates and numerical experiments using an idealized coupled ocean-atmosphere model. (The model has the full three-dimensional primitive equations but has simplified physical parameterizations and geometry.)

Gerber, E. P. and Vallis, G. K., 2009. On the zonal structure of the North Atlantic Oscillation and Annular Modes.

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A numerical and theoretical study of the zonal structure and dipolar patterns in the extratropical atmosphere, and in particular the NAO and annular patterns. The dynamics of such patterns are discussed and it is found that localized NAO-like patterns arise from the confluence of topographic and diabatic forcing and that the patterns are more localized than one would expect based on superposition of the responses to topography and thermal forcing alone.

Zurita-Gotor, P. and Vallis, G. K. 2009. Equilibration of baroclinic turbulence in primitive equation and quasi-geostrophic models.

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Explores the nonlinear equilibration of baroclinic eddies in two-layer PE and QG models. We find that geostrophic turbulence theory has some predictive power for the energy levels etc of the equilibrated turbulent states. We also find that supercritical states and an inverse energy cascade can be found in some parameter regimes (although not those most corresponding to the Earth's atmosphere).

Farneti, R. and Vallis, G. K. 2009. An intermediate complexity climate model based on the GFDL Flexible Modelling System.

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This paper discusses the formulation of a coupled ocean-atmosphere-land-ice model that is much simpler than a full GCM, but still has three-dimensional dynamics and thermodynamics in the atmosphere and ocean.

Vallis, G. K. 2009. Mechanisms of climate variability from years to decades. In press in

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A review article and essay on climate variability. Not so much a literature survey as a discussion of mechanisms, illustrated by examples.

Farneti, R. and Vallis, G. K. 2009. Mechanisms of interdecadal climate variability and the role of ocean-atmosphere coupling

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Explores the mechanisms of decadal climate variability using a simplified, but still fully dynamical, 3D coupled ocean-atmosphere-climate model.

Vallis, G. K. and Gerber, E. P. 2008. Local and Hemispheric Dynamics of the North Atlantic Oscillation, Annular Patterns and the Zonal Index.

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A synthesis of the fundamental dynamics of the NAO and its relation to storm tracks and annular modes/patterns. It also illustrates the phenomena with numerical simulations and with stochastic models.

Zhao, R., and Vallis, G. K. 2008. Parameterizing mesoscale eddies with residual and Eulerian schemes, and a comparison with eddy-permitting models.

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Discusses the use of 'residual' or TEM form of the equations of motion, in an ocean context, especially with regard to parameterizing mesoscale eddies.

Gerber, E. P. and Vallis, G. K. 2007. Eddy-Zonal flow interactions and the persistence of the zonal index.

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Discusses the dynamics of the zonal index, with particular reference to its timescale and interaction with baroclinic eddies.

Zhang, R. and Vallis, G. K. 2007. The role of bottom vortex stretching on the path of the North Atlantic western boundary current and on the northern recirculation gyre.

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Shows that bottom vortex stretching, and the deep western boundary current, influence the Gulf Stream path.

Fuckar, N. S. and Vallis, G. K. 2007. Interhemispheric influence of surface buoyancy conditions on a circumpolar current.

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Demonstrates, using an idealized ocean GCM, that the boundary conditions on surface temperature in the North Atlantic have a strong influence on the zonal transport of the ACC.

Zhang, R. and Vallis, G. K. 2006. Impact of Great Salinity Anomalies on the low frequency variability of the North Atlantic Climate.

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Shows that Great Salt anomalies can potentially alter the Gulf Stream path and influence the climate of the North Atlantic

Pauluis, O. M., Frierson, D. M. W., Garner, S. T., Held, I. M. and G. K. Vallis, 2006. The Hypo-hydrostatic Rescaling and Its Impacts on Modeling of Atmospheric Convection.

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Garner, S. T., Frierson, D. M. W., Held, I. M., Pauluis, O. M. and G. K. Vallis. 2007. Resolving Convection in a Global Hypohydrostatic Model.

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The above two papers explore the so-called hypohydrostatic rescaling, which has the effect of making convection occur at larger scales, and thus leads to a possible 'parameterization' of convection.

Anadadesikan, A, Swathi, P, Slater, R. S. and Vallis, G. K. 2005. Energetics of large-scale ocean circulation.

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Discusses the energetics of the large-scale circulation and its relation to Sandstrom's effect.

Loving, Jolene L., and Geoffrey K. Vallis, 2005. Mechanisms for climate variability during glacial and interglacial periods.

loving-vallis-paleo05.pdf

Offers a mechanism of Dansgaard-Oeschger oscillations. Shows how sea-ice plays an important role.

Dewar, W. D., R. S. Samelson and G. K. Vallis. 2005. The ventilated pool: A model of subtropical mode water.

Dewar-SV05.pdf

Offers an analytic theory of mode water, in the context of thermocline theory and the large-scale circulation

Scaife, A. A., Knight, J. R., Vallis, G. K. and Folland, C. K. 2005. Simulation of observed changes in the North Atlantic Oscillation and surface climate in the latter half of the 20th Century.

Scaife-KVF.pdf

Changes in the NAO over the late 20th century can be simulated properly if the stratosphere is accurately simulated.

Henning, C. and Vallis, G. K. 2005. The Effects of Mesoscale Eddies on the Stratification and Transport of an Ocean with a Circumpolar Channel.

Henning-Vallis05.pdf

Shows, using an idealized eddying ocean model, that mesoscale eddies have a fundamental effect on the stratification of a circumpolar channel, of which the ACC is an example,

Gerber, E. P. and Vallis, G. K., 2005. A stochastic model of the spatial structure of the annular patterns of variability and the NAO.

Gerber-Vallis05.pdf

Demonstrates that the spatial structure -- for example the dipolar structure of the EOFs -- of the NAO can be captured by a simple stochastic model.

Henning, C and Vallis, G. K., 2004. The Effect of mesoscale eddies on the main subtropical thermocline.

Henning_Vallis04.pdf

Discusses and simulates the effects of mesoscale eddies on the main thermocline.

Cash, B., P. Kushner and G. K. Vallis, 2005. Zonal asymmetries, teleconnections and annular modes in a GCM.

Cash-KV05.pdf

Discusses and simulates the relationship between 'annular modes', zonal asymmetries, the storm track, etc., using a simplified GCM.

Vallis, G. K., E. Gerber, P. Kushner and B. Cash. 2004. A mechanism and simple model of the North Atlantic Oscillation and Annular Modes.

Vallis_NAO05.pdf

Offers a simple model of the NAO, and its relationship to the storm tracks and so so-called annular modes.

Griannik, N., I. Held, K.S. Smith and Vallis, G. K. 2004. Effect of nonlinear drag on the inverse cascade. Phys. Fluids 16, 73-78.

Grianik_HSV04.pdf

The halting scale of the inverse cascade in 2D turbulence is independent of the strenght of the turbulence, if a nonlinear drag (such as is common in boundary layer schemes) is used.

Vallis, G. K. Mean and Eddy Dynamics of the Main Thermocline. 2003. In Nonlinear Processes in Geophysical Fluid Dynamics. O. U. Velasco Fuentes, J. Sheinbaum and J. Ochoa (editors). Kluwer Academic Publishers, pp141-173.

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A review and discussion paper on thermocline dynamics, summarizing the work in my papers with Roger Samelson and with Cara Henning, as well as the subject more generally.

Cash, B., P. Kushner and G. K. Vallis. 2002. The structure and composition of the annular modes in an aquaplanet GCM.

Cash_KV02.pdf

By way of numerical simulations with a simplified GCM, shows that 'annular modes' do not necessarily contain annular dynamics. It is just the

Smith, K. S., G. Boccaletti, C. C. Henning, I. Marinov, C. Y. Tam., I. M. Held and G. K. Vallis. 2002. Turbulent diffusion in the geostrophic inverse cascade.

Smith_etal02.pdf

Discusses and simulates the transport properties of the inverse cascade.

Smith, K. S. and G. K. Vallis. 2002. Scales and equilibration of mid-ocean eddies: Forced- dissipative flow.

Smith-Vallis02.pdf

Discusses and simulates the scales of mid-ocean eddies, from the point of view of force-dissipative geostrophic turbulence.

Huck, T., and G. K. Vallis. 2001. Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations.

Huck-Vallis01.pdf

Carries out a three-dimensional linear instabiliot calculation for the THC. Shows that there are unstable modes that resemble the variability in the nonlinear, time-dependent model

Huck, T., G. K. Vallis, and A. Colin de Verdiere. 2001. On the robustness of the inter-decadal modes of the thermohaline circulation.

Huck-Vallis-CdV01.pdf

Explores the robustness of interdecadal variability of the THC.

Smith, K. S. and G. K. Vallis. 2001. Scales and equilibration of mid-ocean eddies. Freely decaying flow.

Smith-Vallis01.pdf

Discusses and simulates the scales of mid-ocean eddies, from the point of view of decaying geostrophic turbulence.

Vallis, G. K. 2000. Thermocline Theories and WOCE: A Mutual Challenge.

Vallis-WOCE.pdf

Brief discussion and overview of thermocline theory and how it might be tested.

Vallis, G. K., 2000. Large-scale circulation and production of stratification: effects of wind, geometry and diffusion.

Vallis2000.pdf

Discusses and simulates the interhemispheric circulation in an idealized, primitive equation, GCM. Shows that the ACC has a profound effect on the circulation. Explores the influence of surface boundary conditions and interhemispheric asymmetries.

Wells, M., G. K. Vallis and E. Silver. Influence of Tectonic Processes in Papua New Guinea on Past Productivity in the Eastern Equatorial Pacific Ocean.

Wells-Silver-Vallis99.pdf

Schonbek, M. and Vallis, G. K. Energy Decay of Solutions to the Boussinesq, Primitive and Planetary Geostrophic Equations.

Schonbek-Vallis99.pdf

Smith, K. S. and G. K. Vallis. Linear wave and instability properties of extended range geostrophic models.

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Calculates the linear wave and baroclinic instability properties of various types of geostrophic model, including quasi-geostrophy, planetary geostrophy, and the so-called geostrophic potential vorticity model that spans QG and PG.

Oetzel, K. and G. K. Vallis. Strain, vortices, and the enstrophy inertial range in two-dimensional turbulence. Phys. Fluids 9, 2991-3004. (1997)

Oetzel-Vallis97.pdf

Shows that a -3 enstrophy inertial range can emerge if the resolution is sufficiently high. Offers a theory for the co-existence of coherent structures with turbulence, and shows that at small scales the coherent vortices will be strained away.

Vallis, G. K., G. J. Shutts, G. and M. E. B. Gray. 1997. Balanced mesoscale motion and stratified turbulence forced by convection.

Vallis-etal97.pdf

Looks at the possible generation of an inverse cascade in low Froude number flow, with he forcing coming from resolved convection at small scales.

Camevale, G., M. Briscolini, R. Kloosterziel, and G.K. Vallis. Three dimensionally perturbed vortex tubes in a rotating flow.

Samelson, R. and G.K. Vallis, 1997. Large-scale circulation with small diapycnal diffusivity: the two-thermocline limit.

Samelson-Vallis.pdf

Proposes that the main thermocline has two dynamical regimes: an adiabatic regime (aka the ventilated themocline), lying above an intrinsically diffusive regime (the internal thermocline). Presents supporting numerical calculations.

Samelson, R. and G.K. Vallis, 1997. A simple fictional and diffusive scheme for the planetary geostrophic equations in a closed basin.

Samelson-Vallis.pdf

Suggests how to make the planetary-geostrophic equations well-posed and numerically efficient in a closed domain. Such a model that was used in the previous reference.

Mundt, M. G.K. Vallis and J. Wang, Balanced models for the large- and meso-scale cir- culation.

Mundt-Vallis-Wang.pdf

Shows how accurate certain PV-based balanced models can be, especially one that bridges the parameter regime between quasi-geostrophy and planetary-geostrophy.

Vallis, G. K. Approximate geostrophic models for large-scale flow in the ocean and atmosphere.

Vallis, G.K., Potential vorticity inversion and balanced equations of motion for rotating and stratified flows.

Vallis96.pdf

Shows how PV inversion can be used to construct higher-order balanced models for strtified flow.

Vallis, G.K. From laminar flow to turbulence. 1996. In:

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Review of various pathways to turbulence (period-doubling, etc.) and of fully-developed turbulence itself.

Warn, T, O. Bokhove, T.G. Shepherd, and G.K. Vallis, Rossby number expansions, slaving, and balance dynamics.

Warn_BSV.pdf

Shows how to construct balanced models of arbitrarily high order, by 'slaving' fields to a single evolving variable, such as potential vorticity.

Cummins, P. and G.K. Vallis, Solvers for separable and non-separable elliptic problems in irregular domains.

Wang, J. and G.K. Vallis, Emergence of Fofonoff states in inviscid and viscous ocean circulation models. J. Mar. Res., 82, 85-127 (1994).

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The so-called Fofonoff solution is the maximum entropy state for two-dimensional flow. This paper explores the statistical mechanical equilibrium of unforced and inviscid ocean models in closed domains, and shows that Fofonoff states do indeed emerge as the time-averaged flow in long integrations.

Vallis, G.K., Statistical mechanics, turbulence, and ocean circulation. in Statistical Methods in Physical Oceanography, `Aha Hulikoa' proceedings, ed. P. Muller and G. Holloway. 473≠491 (1993).

Vallis, G.K. and M. E. Maltrud., 1993. Generation of mean flows and jets on a beta-plane and over topography.

Vallis-Maltrud.pdf

Shows how the beta effect combines with two-dimensional turbulence to give rise to zonal jets. Presents some supporting numerical simulations.

Maltrud. M. and G.K. Vallis, Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence.

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Explores in some detail the energy and enstrophy inertial ranges in 2D turbulence. In particular, the enstrophy transfer is found to be quite nonlocal, in spectral space.

Sundermeyer, M. and G.K. Vallis, Correlation dimension of primitive equation and balanced models.

Sundermeyer-Vallis.pdf

Vallis, G.K., Mechanisms and parameterizations of geostrophic adjustment and a new model for balanced flow.

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Shows that geostrophic balance is the minimum energy state for a given field of potential vorticity, in the linear approximation. Provides a nonlinear extension.

Vallis, G.K., 1992. Problems and phenomenology in two-dimensional turbulence. In: Non-linear Phenomena in Atmospheric and Oceanic Sciences, eds. G. Carnevale and R. Pierrehumbert. 1-25. Springer-Verlag (refereed chapter in book).

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Review of 2D turbulence. Much of this material is now incorporated into textbooks, for example my AOFD book.

Auad, G., A. Pares-Sierra, and G.K. Vallis, 1991. Energetics and diagnostics of a model of the circulation in the California Current System,

Maltrud, M. and G.K. Vallis, 1991. Energy spectra and coherent structures in forced two-dimensional and geostrophic turbulence.

Maltrud-Vallis91.pdf

Shows that the -5/3 inverse energy spectrum of 2D turbulence can be robustly simulated, and determines a value for the Kolmogorov-Kraichnan constant. Also explores effects of simultaneously forcing the fluid at two distinct scales. Shows that an upscale energy spectrum can co-exist, over the same wavenumber range, with a downscale enstrophy cascade.

Carnevale, G.F. and G.K. Vallis, 1990. Iso-vortical energy variation in two-dimensional flows. In: Topological Fluid Mechanics, Proceedings of the IUTAM Symposium, eds. H.K. Moffatt and A. Tsinober. 294-303 (refereed conference proceedings).

Vallis, G.K., G.F. Carnevale, and T.G. Shepherd, 1990. A natural method for the stable states of Hamiltonian systems. In: Topological Fluid Mechanics, Proceedings of the IUTAM Symposium, eds. H.K. Moffatt and A. Tsinober. 429-439 (refereed conference proceedings).

Carnevale, G.F. and G.K. Vallis, 1990. Pseudo-advective relaxation to stable two-dimensional states.

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Vallis, G.K., G.F. Carnevale, and W.R. Young, 1989. Extremal energy properties and construction of stable solutions of the Euler equations.

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Shows how a modification of the Euler equations of motion can be made that causes the modified system to monotonically increase in energy, while keeping the Casimirs (e.g. enstrophy) constant. Thus can be used to construct Arnold stable states.

Pares-Sierra, A. and G.K. Vallis, 1989. A fast semi-direct method for the numerical solution of non-separable elliptic equations in irregular domains.

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Describes a fast method to solve non-separable elliptic equations in irregular domains. Combines the capacitance matrix method with a fast iteration.

Carnevale, G.F., R. Purini, M. Briscolini, and G.K. Vallis, 1989. Influence of topography on modon propagation and survival. In: Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence, eds. J.C.J. Nihoul and B.M. Jamart. Elsevier Science Publishers (invited review article).

Vallis, G.K., 1988. Conceptual models of El Nino and the Southern Oscillation.

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Discusses whether El Nino and ENSO is a chaotic or stochastic system, and proposes example models of both.

Carnevale, G. F., R. Purini, M. Briscolini, and G.K. Vallis, Numerical experiments on modon stability to topographic perturbations.

Carnevale, G.F., G.K. Vallis, R. Purini, and M. Briscolini, 1988. The role of initial conditions in flow stability, with applications to modons.

Vallis, G.K., 1988. A numerical study of transport properties in eddy resolving and parameterized models.

Vallis_QJ88.pdf

Studies how the heat transport varies with the imposed temperature gradient in a numerical model of QG turbulence, and compares to possible parameterization schemes.

Carnevale, G.F., G.K. Vallis, R. Purini, and M. Briscolini, Propagation of barotropic modons over topography.

Vallis, G.K. and B.-L. Hua, Eddy viscosity of the anticipated potential vorticity method.

Vallis, G.K., El Nino: A chaotic dynamical system? Science, 232, 243-245 (1986).

Vallis86.pdf

Suggests that El Nino might be a chaotic dynamical system, and presents a simple model to illustrate this.

Vallis, G.K. and J.O. Roads, Turbulent effects in large scale flow over topography. In: Proceedings of Second International Symposium on Tibet Plateau and Mountain Meteorology, Beijing, eds. Z. Baozhen and E. Reiter. 390-407, Academia Sinica, China (conference proceedings) (1986).

Vallis, G.K., Instability and flow over topography.

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Performs a linear stability analysis of flow over topography and of stationary waves, using a long-wave approximation and triad interactions. Also shows that the Charney-Stern-like criterion for instability in a 2-layer model also applies to finite-amplitude disturbances.

Vallis, G.K., Remarks on the predictability properties of two- and three-dimensional flow.

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Provides a theoretical discussion of the predictability properties of 2D and 3d turbulence. Some of this material is now incorporated into my AOFD book.

Vallis, G.K., On the spectral integration of the quasi-geostrophic equations for doubly-periodic and channel flow.

Vallis, G.K. and J.O. Roads, 1984. Large-scale stationary and turbulent flow over topography.

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In this paper we compare linear theory of flow over topography with the results from a time-dependent, nonlinear, unsteady, simulation of the same flow. Generally, the instabilities extract energy from the stationary waves, reducing the amplitude of the response from that given by linear theory.

Roads, J.O., G.K. Vallis, and L. Remer, Cloud/climate sensitivity experiments. In: Climate Processes and Climate Sensitivity, 92-107. Geophysical Monograph 29, eds. J. Hansen and T. Takahashi. American Geophysical Union (refereed article in book) (1984).

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This paper looked at the relationship between the large-scale circulation and large-scale clouds, using a model that had explicit evolution equations for water vapour and cloud water but otherwise idealized dynamics.

Roads, J.O. and G.K. Vallis, 1984. An energy balance model with cloud feedbacks.

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Most EBMs have specified clouds. This is an attempt to construct and learn something from an EBM in which clouds are predicted.

Carnevale, G.F. and G.K. Vallis, Applications of entropy to predictability theory.

Vallis, G. K., Barotropic and baroclinic predictability in geostrophic turbulence.

Vallis, G.K., On the predictability of quasigeostrophic flow: the effects of beta and baroclinicity.

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Discusses and simulates how baroclinic instability and the beta effect will affect predictability.

Cayan, D., R. Harnack, and G.K. Vallis, Report on workshop on weather and climate variability during winter 1981-1982.

Vallis, G.K., A statistical dynamical climate model with a simple hydrology cycle.

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Describes a zonally-averaged near-primitive-equation (actually semi-geostrophic) model, using Green-like parameterizations for eddy transport. Adds an equation for moisture (i.e., a hydrology cycle) and explores the effects.