arXiv subjects

Geoffrey K. Vallis

Publications and source records attributed to Geoffrey K. Vallis.

13 recordsLinked to original sources

arXiv2026

Influence of penetration depth on jets on giant planets: equatorial jet direction, jet numbers, and jet energy fraction

It remains puzzling why, despite their similar nature, Jupiter and Saturn possess a prograde equatorial jet, whereas Uranus and Neptune have a retrograde one. To understand this discrepancy, we use a two-dimensional quasi-geostrophic model to explore how the jet penetration depth, regulated by Ohmic dissipation, influences the structure and organization of jet patterns. When jets penetrate deeply into the planetary interior, the effective planetary vorticity gradient $β$ becomes negative near the equator and decreases equatorward due to spherical geometry. This $β$ profile favors dynamical modes that transport eastward momentum toward the equator, producing a prograde equatorial jet, as observed on Jupiter and Saturn. In contrast, relatively shallow systems favor a retrograde equatorial jet. In our simulations, the equatorial jet direction is primarily controlled by the gradient of $β$, as predicted by Stochastic Structural Stability Theory, rather than by its sign, as suggested by Potential Vorticity mixing. If this mechanism applies to Uranus and Neptune, the observed jet structure may suggest the presence of a stratified or Ohmic dissipation layer near their surfaces. At mid-latitudes, jet widths are constrained by the Rhines scale, yielding a scaling that explains the presence of multiple jets on Jupiter and Saturn and a single jet per hemisphere on Uranus and Neptune. Lastly, we examine how planetary parameters influence the partitioning of energy between jets and eddies. Stronger energy input, faster rotation, smaller planetary radius, or weaker large-scale damping lead to a larger fraction of the total energy in zonal jets, resulting in smoother jet structures.

astro-ph.EP↗

arXiv2025

Mechanisms of Superrotation in Slowly-Rotating and Tidally-Locked Planets

Superrotation is a common feature of quickly rotating gas giants, slowly rotating planetary bodies, and tidally-locked planets. In this paper we compare and contrast the mechanisms of superrotation in slow rotators and tidally-locked planets. We cover a wide range of planetary properties, varying in particular the thermal Rossby number Ro_T (controlled by planetary size, rotation rate, and instellation) and a radiative relaxation timescale T_rad (which parameterizes atmospheric optical thickness). We use a two-level model that contains the principal mechanisms for superrotation in both regimes yet remains analytically tractable. Linearizations of the model elucidate the behavior of superrotation-inducing eddies. In tidally-locked planets a Matsuno-Gill-like structure organizes the eddy effects but of itself is insufficient to produce superrotation; baroclinicity and low-level drag are additional essential ingredients. Nonlinear integrations further explore the superrotating regimes and exhibit significant time variability even in statistical equilibrium. Not all tidally-locked regimes superrotate: subrotation arises at high T_rad (optically thick atmospheres) and weak low-level drag. On axisymmetrically-forced slow rotators, superrotation is always linked to a previously identified Rossby-Kelvin instability. Perhaps surprisingly, the instability itself is also linked to the spinup of superrotation in some tidally-locked regimes. Finally, we explore the continuous transition in the mechanisms of superrotation from axisymmetrically-forced to tidally-locked planets by applying a progressively stronger asymmetric equatorial forcing. The Matsuno-Gill pattern quickly dominates over traveling planetary Rossby-Kelvin waves in forcing superrotation, although both mechanisms can coexist. These results provide a unified view of superrotation mechanisms across a wide range of planetary bodies.

astro-ph.EP↗

arXiv2024

Boiling stratified flow: a laboratory analogy for atmospheric moist convection

We present a novel laboratory experiment, boiling stratified flow, as an analogy for atmospheric moist convection. A layer of diluted syrup is placed below freshwater in a beaker and heated from below. The vertical temperature profile in the experiment is analogous to the vapor mixing ratio in the atmosphere while the vertical profile of freshwater concentration in the experiment is analogous to the potential temperature profile in the atmosphere. Boiling starts when the bottom of the syrup layer reaches the boiling point, producing bubbles and vortex rings that stir the two-layer density interface and bring colder fresh water into the syrup layer. When the syrup layer at the beginning of the experiment is sufficiently thin and diluted, the vortex rings entrain more cold water than needed to remove superheating in the syrup layer, ending the boiling. When the syrup layer is deep and concentrated, the boiling is steady since the entrained colder water instantaneously removes the superheating in the bottom syrup layer. A theory is derived to predict the entrainment rate and the transition between the intermittent and steady boiling regimes, validated by experimental data. We suggest that these dynamics may share similarities with the mixing and lifecycle of cumulus convection.

physics.flu-dyn↗

arXiv2020

The Trouble with Water: Condensation, Circulation and Climate

This article discussesl a few of the problems that arise in geophysical fluid dynamics and climate that are associated with the presence of moisture in the air, its condensation and release of latent heat. Our main focus is Earth's atmosphere but we also discuss how these problems might manifest themselves on other planetary bodies, with particular attention to Titan where methane takes on the role of water. GFD has traditionally been concerned with understanding the very basic problems that lie at the foundation of dynamical meteorology and ocean\-ography. Conventionally, and a little ironically, the subject mainly considers `dry' fluids, meaning it does not concern itself overly much with phase changes. The subject is often regarded as dry in another way, because it does not consider problems perceived as relevant to the real world, such as clouds or rainfall, which have typically been the province of complicated numerical models. Those models often rely on parameterizations of unresolved processes, parameterizations that may work very well but that often have a semi-empirical basis. The consequent dichotomy between the foundations and the applications prevents progress being made that has both a secure basis in scientific understanding and a relevance to the Earth's climate, especially where moisture is concerned. The dichotomy also inhibits progress in understanding the climate of other planets, where observations are insufficient to tune the parameterizations that weather and climate models for Earth rely upon, and a more fundamental approach is called for. Here we discuss four diverse examples of the problems with moisture: the determination of relative humidity and cloudiness; the transport of water vapor and its possible change under global warming; the moist shallow water equations and the Madden-Julian Oscillation; and the hydrology cycle on other planetary bodies.

physics.ao-ph↗

arXiv2019

Meridional Structure and Future Changes of Tropopause Height and Temperature

We use a simple, semi-analytic, column model to better understand the meridional structure of the tropopause height and the future changes in its height and temperature associated with global warming. The model allows us to separate the effects of tropospheric lapse rate (TLR), optical depth, outgoing longwave radiation (OLR) and stratospheric cooling on the tropopause height. When applied locally at each latitudinal band the model predicts the overall meridional structure of the tropopause height, with a tropical tropopause substantially higher than that in higher latitudes and a sharp transition at the edge of the extratropics. The large optical depth of the tropics, due mainly to the large water vapour path (WVP), is the dominant tropospheric effect producing the higher tropical tropopause, whereas the larger tropical lapse rate acts to lower the tropopause height. The dynamical cooling induced by the stratospheric circulation further lifts the thermal tropopause in the tropics resulting in it being significantly cooler and higher than in mid- and high latitudes. The model quantifies the causes of the tropopause height increase with global warming that is robustly found in climate integrations from the fifth Coupled Model Intercomparison Project (CMIP5). The large spread in the increase rate of tropopause height in the CMIP5 models is captured by the simple model, which attributes the dominant contributions to changes in WVP and TLR, with changes in CO2 concentration and OLR having much smaller effects. The CMIP5 models also show a small but robust increase in the tropopause temperature in low latitudes, with a much smaller increase in higher latitudes. We suggest that the tropical increase may in part be caused by non-grey effects in the radiative transfer associated with the higher levels of water vapour in the tropics, with near constant tropopause temperatures predicted otherwise.

physics.ao-ph↗

arXiv2019

The Effects of Gravity on the Climate and Circulation of a Terrestrial Planet

The climate and circulation of a terrestrial planet are governed by, among other things, the distance to its host star, its size, rotation rate, obliquity, atmospheric composition and gravity. Here we explore the effects of the last of these, the Newtonian gravitational acceleration, on its atmosphere and climate. We first demonstrate that if the atmosphere obeys the hydrostatic primitive equations, which are a very good approximation for most terrestrial atmospheres, and if the radiative forcing is unaltered, changes in gravity have no effect at all on the circulation except for a vertical rescaling. That is to say, the effects of gravity may be completely scaled away and the circulation is unaltered. However, if the atmosphere contains a dilute condensible that is radiatively active, such as water or methane, then an increase in gravity will generally lead to a cooling of the planet because the total path length of the condensible will be reduced as gravity increases, leading to a reduction in the greenhouse effect. Furthermore, the specific humidity will decrease, leading to changes in the moist adiabatic lapse rate, in the equator-to-pole heat transport, and in the surface energy balance because of changes in the sensible and latent fluxes. These effects are all demonstrated both by theoretical arguments and by numerical simulations with moist and dry general circulation models.

astro-ph.EP↗

arXiv2018

A Simple System for Moist Convection: the Rainy-Benard Model

Raylaigh-Benard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of atmospheric convection is the buoyancy source provided by the condensation of water vapour, but the presence of radiation, compressibility, liquid water and ice further complicate the system and our understanding of it. In this paper we present an idealized model of moist convection by taking the Boussinesq limit of the ideal gas equations and adding a condensate that obeys a simplified Clausius--Clapeyron relation. The system allows moist convection to be explored at a fundamental level and reduces to the classical Rayleigh-Benard model if the latent heat of condensation is taken to be zero. The model has an exact, Rayleigh-number independent `drizzle' solution in which the diffusion of water vapour from a saturated lower surface is balanced by condensation, with the temperature field (and so the saturation value of the moisture) determined self-consistently by the heat released in the condensation. This state is the moist analogue of the conductive solution in the classical problem. We numerically determine the linear stability properties of this solution as a function of Rayleigh number and a nondimensional latent-heat parameter. We also present a number of turbulent solutions.

physics.ao-ph↗

arXiv2018

A Stochastic Lagrangian Basis for a Probabilistic Parameterization of Moisture Condensation in Eulerian Models

In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation---in which condensation occurs---that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will be underestimated. On the other hand, in a stochastic Lagrangian model of moisture transport, trajectories of parcels tagged with humidity variables are tracked and small-scale moisture variability can be retained; however, explicitly implementing such a scheme in a global model would be computationally prohibitive. One way to introduce subgrid-scale saturation into an Eulerian model is to assume the humidity within a grid box has a probability distribution. To close the problem, this distribution is conventionally determined by relating the required subgrid-scale properties of the flow to the grid-scale properties using a turbulence closure. Here, instead, we determine an assumed probability distribution by using the statistical moments from a stochastic Lagrangian version of the system. The stochastic system is governed by a Fokker--Planck equation and we use that, rather than explicitly following the moisture parcels, to determine the parameters of the assumed distribution. We are thus able to parameterize subgrid-scale condensation in an Eulerian model in a computationally efficient and theoretically well-founded way. In two idealized advection--condensation problems we show that a coarse Eulerian model with the subgrid parameterization is well able to mimic its Lagrangian counterpart.

physics.ao-ph↗

arXiv2017

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach

A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique due to a gauge freedom. Here, it is argued that a Galilean invariant subfilter scale (SFS) flux is a suitable quantity to properly measure energy scale-transfer in the Ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale-transfer of energy. The paper presents geographic maps of the energy scale-transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions, near the Gulf Stream and in the Equatorial Counter Current have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extra-tropical energy scale-transfer over regions of O(10^3) kilometers in size.

physics.flu-dyn↗

arXiv2017

The thermal phase curve offset on tidally- and non-tidally-locked exoplanets: A shallow water model

Using a shallow water model with time-dependent forcing we show that the peak of an exoplanet thermal phase curve is, in general, offset from secondary eclipse when the planet is rotating. That is, the planetary hot-spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset is a function of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady-state in the reference frame of the moving forcing. The model is an extension of the well studied Matsuno-Gill model into a full spherical geometry and with a planetary-scale translating forcing representing the insolation received on an exoplanet from a host star. The speed of the gravity waves in the model is shown to be a key metric in evaluating the phase curve offset. If the velocity of the substellar point (relative to the planet's surface) exceeds that of the gravity waves then the hotspot will lag the substellar point, as might be expected by consideration of forced gravity wave dynamics. However, when the substellar point is moving slower than the internal wavespeed of the system the hottest point can lead the passage of the forcing. We provide an interpretation of this result by consideration of the Rossby and Kelvin wave dynamics as well as, in the very slowly rotating case, a one-dimensional model that yields an analytic solution. Finally, we consider the inverse problem of constraining planetary rotation rate from an observed phase curve.

astro-ph.EP↗

arXiv2014

Ribbon Turbulence

We investigate the non-linear equilibration of a two-layer quasi-geostrophic flow in a channel forced by an imposed unstable zonal mean flow, paying particular attention to the role of bottom friction. In the limit of low bottom friction, classical theory of geostrophic turbulence predicts an inverse cascade of kinetic energy in the horizontal with condensation at the domain scale and barotropization on the vertical. By contrast, in the limit of large bottom friction, the flow is dominated by ribbons of high kinetic energy in the upper layer. These ribbons correspond to meandering jets separating regions of homogenized potential vorticity. We interpret these result by taking advantage of the peculiar conservation laws satisfied by this system: the dynamics can be recast in such a way that the imposed mean flow appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent flow that stirs this potential vorticity field while conserving the global distribution of potential vorticity levels. Statistical mechanical theory of the 1-1/2 layer quasi-geostrophic model predict the formation of two regions of homogenized potential vorticity separated by a minimal interface. We show that the dynamics of the ribbons results from a competition between a tendency to reach this equilibrium state, and baroclinic instability that induces meanders of the interface. These meanders intermittently break and induce potential vorticity mixing, but the interface remains sharp throughout the flow evolution. We show that for some parameter regimes, the ribbons act as a mixing barrier which prevent relaxation toward equilibrium, favouring the emergence of multiple zonal jets.

physics.flu-dyn↗

arXiv2012

The catalytic role of beta effect in barotropization processes

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e., the tendency to reach the gravest vertical mode. The peculiar role of the $β$-effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing $β$ increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropisation may be partly parameterized using the Rhines scale $2πE_{0}^{1/4}/β^{1/2}$. As this parameter decreases (beta increases) then barotropization can progress further, because the beta term provides enstrophy to each layer.

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arXiv2010

The Transition to Superrotation in Terrestrial Atmospheres

We show that by changing a single non-dimensional number, the thermal Rossby number, global atmospheric simulations with only axisymmetric forcing pass from an Earth-like atmosphere to a superrotating atmosphere that more resembles the atmospheres of Venus or Titan. The transition to superrotation occurs under conditions in which equatorward-propagating Rossby waves generated by baroclinic instability at intermediate and high latitudes are suppressed, which will occur when the deformation radius exceeds the planetary radius. At large thermal Rossby numbers following an initial, nearly axisymmetric phase, a global baroclinic wave of zonal wavenumber one generated by mixed barotropic-baroclinic instability dominates the eddy flux of zonal momentum. The global wave converges eastward zonal momentum to the equator and deposits westward momentum at intermediate latitudes during spinup and before superrotation emerges, and the baroclinic instability ceases once superrotation is established. A global barotropic mode of zonal wavenumber one generated by a mix of high- and low-latitude barotropic instability is responsible for maintaining superrotation in the statistically steady state. At intermediate thermal Rossby numbers, momentum flux by the global baroclinic mode is subdominant relative to smaller baroclinic modes, and thus strong superrotation does not develop.

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