On the maintenance of thermal wind balance and equatorial superrotation in Titan's stratosphere

Titan's atmospheric winds, like those on Venus, exhibit superrotation at high altitudes. Titan general circulation models have yielded conflicting results on whether prograde winds in excess of 100 m s⁻¹ at the 1 mbar level are possible based on known physical processes that drive wind systems. A comprehensive two-dimensional (2D) model for Titan's stratosphere was constructed to systematically explore the physical mechanisms that produce and maintain stratospheric wind systems. To ensure conservation of angular momentum in the limit of no net exchange of atmospheric angular momentum with the solid satellite and no external sources and sinks, the zonal momentum equation was solved in flux form for total angular momentum. The relationships among thermal wind balance, meridional circulation, and zonal wind were examined with numerical experiments over a range of values for fundamental input parameters, including planetary rotation rate, radius, internal friction due to wave stresses, and net radiative drive. The magnitude of mid-latitude jets is most sensitive to a single parameter, the planetary rotation rate and results from the conversion of planetary angular momentum to relative angular momentum by the meridional circulation, whereas the strength of meridional circulation is mainly determined by the magnitude of the radiative drive. For Titan's slowly rotating atmosphere, the meridional temperature gradient is vanishingly small, even when the radiative drive is enhanced beyond reasonable magnitudes, and can be inferred from zonal winds in gradient/thermal wind balance. In our 2D model large equatorial superrotation in Titan's stratosphere can be only produced through internal drag forcing by eddy momentum fluxes, which redistribute angular momentum within the atmosphere, while still conserving the total angular momentum of the atmosphere with time. We cannot identify any waves, such as gravitational or thermal tides, that are sufficiently capable of generating the required eddy forcing of >50 m s⁻¹ Titan-day⁻¹ to maintain peak prograde winds in excess of 100 m s⁻¹ at the 1 mbar level.     

Some problems of Venus' atmospheric dynamics

A brief survey is given of the observational data on wind speeds in the atmosphere of Venus, as well as results of the theory of similitude and of a scale analysis for estimation of the wind speeds and temperature contrasts. It is shown that, in the lower portion of the atmosphere, containing roughly half of the mass, the first method produces results which are in somewhat better agreement with the measurements. Measurements of the wind distribution in the atmosphere are discussed. It is shown that, in the slowly rotating atmosphere of Venus, we should expect the Solberg mechanism of inertial instability of the circulation to be effective with respect to axisymmetrical perturbations. The numerical experiments of G.P. Williams (1968, J. Atmos. Sci., 25, 34–1045; 1970, Geophys. Fluid Dyn., 1, 357–369) indicate that in this case the circulation in the meridional plane can be broken down into a series of forward and reverse cells. The existence of such cells can serve to preserve the angular momentum of the planet with its atmosphere—the total momentum of the atmospheric frictional forces against the surface should on the average equal zero. This supports the hypothesis of G. Schubert et al. (1980, J. Geophys. Res., 85, 8007–8025) concerning the multicellular structure of the meridional circulation. Data are analyzed with regard to the time variability of the circulation. If the angular momentum of Venus′ atmosphere can change by 30% (which is not excluded by the presently available data; in Earth's atmosphere seasonal variations of the momentum reach 50%), then the relative variations in the length of a Venusian day will attain 10^?3, i.e., several hours. The surface boundary layer is considered. It is shown that, due to the small transparency of the atmosphere to thermal radiation, heat transfer between the surface and the atmosphere should basically take place by turbulent heat exchange. The basic parameters of the dynamic and thermal regimes of this layer are estimated. Questions of light refraction in the boundary layer are discussed. A strict theory of refraction, developed for these conditions, confirms the preliminary rough estimates of V.I. Moroz (1976, Cosmic Res., 14, No. 5, 691–692; Space Sci. Rev., 25, 3–127), viz, that the horizon is visible on the panorama at a distance of order 100m, due to a relatively sharp negative gradient near the surface.     

Near-surface winds at the Huygens site on Titan: Interpretation by means of a general circulation model

This study aims at interpreting the zonal and meridional wind in Titan's troposphere measured by the Huygens probe by means of a general circulation model. The numerical simulation elucidates the relative importance of the seasonal variation in the Hadley circulation and Saturn's gravitational tide in affecting the actual wind profile. The observed reversal of the zonal wind at two altitudes in the lower troposphere can be reproduced with this model only if the near-surface temperature profile is asymmetric about the equator and substantial seasonal redistribution of angular momentum by the variable Hadley circulation takes place. The meridional wind near the surface is mainly caused by the meridional pressure gradient and is thus a manifestation of the Hadley circulation. Southward meridional wind in the PBL (planetary boundary layer) is consistent with the near-surface temperature at the equator being lower than at mid southern latitudes. Even small changes in the radiative heating profile in the troposphere can substantially affect the mean zonal and meridional wind including their direction. Saturn's gravitational tide is rather weak at the Huygens site due to the proximity to the equator, and does not clearly manifest itself in the instantaneous vertical profile of wind. Nevertheless, the simulated descent trajectory is more consistent with the observation if the tide is present. Because of a different force balance in Titan's atmosphere from terrestrial conditions, PBL-specific wind systems like on Earth are unlikely to exist on Titan.     

Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales

Atmospheric angular momentum variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. The exchange of angular momentum between the fluid layers and the solid planet is the main cause for the variations of the planetary rotation at seasonal time scales. In the present study, we investigate the angular momentum variations of the Earth, Mars and Venus, using geodetic observations, output of state-of-the-art global circulation models as well as assimilated data. We discuss the similarities and differences in angular momentum variations, planetary rotation and angular momentum exchange for the three terrestrial planets. We show that the atmospheric angular momentum variations for Mars and Earth are mainly annual and semi-annual whereas they are expected to be “diurnal” on Venus. The wind terms have the largest contributions to the LOD changes of the Earth and Venus whereas the matter term is dominant on Mars due to the CO₂ sublimation/condensation. The corresponding LOD variations (ΔLOD) have similar amplitudes on Mars and Earth but are much larger on Venus, though more difficult to observe.     

Decadal variations in a Venus general circulation model

The Community Atmosphere Model (CAM), a 3-dimensional Earth-based climate model, has been modified to simulate the dynamics of the Venus atmosphere. The most current finite volume version of CAM is used with Earth-related processes removed, parameters appropriate for Venus introduced, and some basic physics approximations adopted. A simplified Newtonian cooling approximation has been used for the radiation scheme. We use a high resolution (1° by 1° in latitude and longitude) to take account of small-scale dynamical processes that might be important on Venus. A Rayleigh friction approach is used at the lower boundary to represent surface drag, and a similar approach is implemented in the uppermost few model levels providing a ‘sponge layer’ to prevent wave reflection from the upper boundary. The simulations generate superrotation with wind velocities comparable to those measured in the Venus atmosphere by probes and around 50-60% of those measured by cloud tracking. At cloud heights and above the atmosphere is always superrotating with mid-latitude zonal jets that wax and wane on an approximate 10 year cycle. However, below the clouds, the zonal winds vary periodically on a decadal timescale between superrotation and subrotation. Both subrotating and superrotating mid-latitude jets are found in the approximate 40-60 km altitude range. The growth and decay of the sub-cloud level jets also occur on the decadal timescale. Though subrotating zonal winds are found below the clouds, the total angular momentum of the atmosphere is always in the sense of superrotation. The global relative angular momentum of the atmosphere oscillates with an amplitude of about 5% on the approximate 10 year timescale. Symmetric instability in the near surface equatorial atmosphere might be the source of the decadal oscillation in the atmospheric state. Analyses of angular momentum transport show that all the jets are built up by poleward transport by a meridional circulation while angular momentum is redistributed to lower latitudes primarily by transient eddies. Possible changes in the structure of Venus’ cloud level mid-latitude jets measured by Mariner 10, Pioneer Venus, and Venus Express suggest that a cyclic variation similar to that found in the model might occur in the real Venus atmosphere, although no subrotating winds below the cloud level have been observed to date. Venus’ atmosphere must be observed over multi-year timescales and below the clouds if we are to understand its dynamics.     

General atmospheric circulation driven by polar and diurnal surface temperature variations

Described is a global circulation model for the Venus atmosphere that includes the effects of both polar cooling and diurnal temperature variation. It is based on a linearized Boussinesq approximation and boundary conditions derived from theoretical and empirical considerations. The time-dependent, three-dimensional flow field is deduced without any a priori assumptions about its configuration. Results show that the mean atmospheric motions are essentially zonal in a narrow belt near the equator and change to become meridional over most of the globe. The circulation pattern is not symmetrical and rotates about the polar axis of the planet with the period of the solar day.     

The effects of vigorous mixing in a convective model of zonal flow on the ice giants

Previous studies have used models of three-dimensional (3D) Boussinesq convection in a rotating spherical shell to explain the zonal flows on the gas giants, Jupiter and Saturn. In this paper we demonstrate that this approach can also generate flow patterns similar to those observed on the ice giants, Uranus and Neptune. The equatorial jets of Uranus and Neptune are often assumed to result from baroclinic cloud layer processes and have been simulated with shallow layer models. Here we show that vigorous, 3D convection in a spherical shell can produce the retrograde (westward) equatorial flows that occur on the ice giants as well as the prograde (eastward) equatorial flows of the gas giants. In our models, the direction of the equatorial jet depends on the ratio of buoyancy to Coriolis forces in the system. In cases where Coriolis forces dominate buoyancy, cylindrical Reynolds stresses drive prograde equatorial jets. However, as buoyancy forces approach and exceed Coriolis forces, the cylindrical nature of the flow is lost and 3D mixing homogenizes the fluid's angular momentum; the equatorial jet reverses direction, while strong prograde jets form in the polar regions. Although the results suggest that conditions involving strong atmospheric mixing are responsible for generating the zonal flows on the ice giants, our present models require roughly 100 and 10 times the internal heat fluxes observed on Uranus and Neptune, respectively.     

Vertical extent of zonal winds on Venus

Possible interrelationships of different observations have been studied to clear up some obvious inconsistencies and develop a coherent picture of the kinematics of the Venus atmosphere. There is a wind shear in the vicinity of 60 km with vertical dimensions on the order of a scale height. The kinematical model has negligible surface winds, speeds increasing with altitude to approximately 45 km, a layer of high-speed retrograde zonal winds extending from approximately 45 to 60 km, a wind shear between 60 and 65 km, and slow atmospheric motions above this. Spacecraft data show that the region of high-speed winds is thicker on the day side of the planet than on the night side.     

Dynamical aspects of the venus 4-day circulation

Evidence for the 4-day retrograde zonal circulation of the upper Venus atmosphere is summarized. The ‘moving flame’ phenomenon, convective instability to a mean shear and tidal forcing are discussed as possible dynamical explanations for the 4-day rotation. Tidal forcing seems feasible only if momentum diffusion is molecular in nature. Convective instability to a mean shear, although it can account for the magnitude of the 4-day circulation, must be supplemented by another mechanism, the ‘moving flame’ say, to explain the direction of the zonal motion. However, numerical computations indicate that the ‘moving flame’ by itself can account for both the magnitude and direction of the 4-day rotation. It appears that the stable stratification above altitudes of about 60 km is an essential factor in the ‘moving flame’ mechanism for generating the retrograde atmospheric rotation.     

Simulations of Superrotation on Slowly Rotating Planets: Sensitivity to Rotation and Initial Condition

We use a simplified terrestrial general circulation model as a nonlinear process model to investigate factors that influence the extent of equatorial superrotation in statically stable atmospheres on slowly rotating planets such as Titan and Venus. The possibility of multiple equilibria is tested by running the same model to equilibrium from vastly different initial conditions. The final state is effectively independent of initial state, reinforcing the impression that equatorial superrotation is inevitable on slowly rotating planets with stable radiative equilibrium structures. Of particular interest is the fact that at Titan rotation, the model equilibrates with strong prograde winds even when initialized with strong retrograde winds. This suggests that reliable remote sensing inferences of latitudinal temperature gradients on Titan can unambiguously be interpreted as evidence for superrotation. We also demonstrate for the first time that significant equatorial superrotation can be produced at Venus' rotation rate in such models, given sufficient numerical precision. The strength of superrotating zonal winds increases with rotation rate in the slowly rotating regime when other parameters are held fixed. However, the efficiency of superrotation relative to the angular momentum of an atmosphere corotating with the solid planet increases with decreasing rotation rate instead, because the Hadley cell strengthens and expands poleward. This allows for the formation of stronger high latitude jets, which ultimately serve as the source for equatorial superrotation via barotropic instability. Estimates of relevant parameter settings for Triton and Pluto tentatively imply that their atmospheres may marginally be in the superrotating regime, but only if temperature decreases with height near the surface.     

Tidal Winds on Titan Caused by Saturn

The influence of Saturn's gravitational tide on the atmosphere of Titan is investigated by means of a three-dimensional general circulation model. Titan's orbital eccentricity of 0.0292 gives rise to time-dependent radial and librational tide whose potential circles eastward on Titan. Unlike atmospheric tides on terrestrial planets, Saturn's tide on Titan has a large impact on the dynamic meteorology down to the surface. The surface pressure oscillates by up to 1.5 hPa through the orbit. Near the surface the tidal wind dominates the atmospheric flow and exhibits strong temporal and spatial variation. The superposition of the annually present, thermally forced latitudinal pressure gradient and tidally caused pressure variation produces a unique wind pattern near the surface characterized by equatorward flow and high-latitude whirls. At higher levels the tidal wind manifests itself as eastward traveling planetary-scale wave of wavenumber 2 superposed on the background wind. In general tidal winds are more significant in the troposphere, where other forcing mechanisms are weak. Meridional tidal winds become as fast as 5 m s⁻¹ in the troposphere and change direction periodically through the orbit and along the parallel of latitude. Except in the lower troposphere, zonal winds always remain prograde because the tidal wind amplitude is usually smaller than the mean zonal wind. The tide also has a large impact on the mean zonal circulation in the stratosphere. A meridional drift of the descending Huygens Probe in the troposphere would be the easiest way to verify the tidal wind on Titan, but more complete observations of tropospheric wind and surface pressure by a future mission would be required to unveil the complete details of the tidal wind.     

A zonal-averaged dynamical model for the middle atmosphere including gravity wave mean flow interaction: Solstice conditions

Using a set of transformed Eulerian equations the zonal-averaged circulation of the middle atmosphere (10–110 km) is calculated on a global scale for solstice conditions. The emphasis lies on an improved modelling of the zonal momentum balance of the mesophere and lower thermosphere. For this purpose an internal gravity wave mean flow interaction model suggested by T. Matsuno has been incorporated in a slightly modified version. With this model the observed reversal of the zonal wind with height in the summer upper mesosphere and lower thermosphere can be reproduced. The coefficient of eddy momentum diffusion and the Rayleigh friction coefficient used in this model have been made temperature dependent by describing them as a function of the local static stability parameter.     

Influence of the Atmospheric Tides on the Earth Rotation

Spectral analysis of the components of the relative atmospheric angular momentum vector is performed based on the series of these components for the 6 h intervals within the period of 1958–2000. These series have been computed in the Subbureau of the Atmospheric Angular Momentum of the International Earth Rotation Service using the NCEP/NCAR reanalysis of atmospheric observations. The basic harmonics of diurnal tides are determined. New results on the fortnight's and week's duration oscillations of the equatorial components of the atmospheric angular momentum are obtained. The zonal tides transformation mechanisms in the atmosphere are discussed. It is shown that the main mechanism of the zonal tides effect on the atmospheric variability is the amplitude modulation of daily oscillations of the relative atmospheric angular momentum. The effects of the atmospheric tides on the Earth rotation are discussed.     

Observation of a tilt of Titan's middle-atmospheric superrotation

Maps of isotherms on surfaces of constant pressure in Titan's middle atmosphere encircle the poles but show an offset, implying that the mean zonal flow has an axis of symmetry that is tilted relative to the spin axis of the solid body. The effect is seen in both hemispheres around a consistent axis. Periodogram analysis of the temperature field shows that wavenumber one, the signal corresponding to the spin tilt, is the strongest wave component. We conjecture that the tilt of the atmospheric spin is due to a feedback between the flow and the solar heating. The spin adjusts itself to align the spin equator with the direction toward the Sun, and thereby maximizes the efficiency with which the meridional circulation pumps angular momentum upward to generate superrotation.     

Zonal winds at high latitudes on Venus: An improved application of cyclostrophic balance to Venus Express observations

Recent retrievals of zonal thermal winds obtained in a cyclostrophic regime on Venus are generally consistent with cloud tracking measurements at mid-latitudes, but become unphysical in polar regions where the values obtained above the clouds are often less than or close to zero. Using a global atmospheric model, we show that the main source of errors that appear in the polar regions when retrieving the zonal thermal winds is most likely due to uncertainties in the zonal wind intensity in the choice of the lower boundary condition.Here we suggest a new and robust method to better estimate the lower boundary condition for high latitudes, thereby improving the retrieved zonal thermal winds throughout the high latitudes middle atmosphere. This new method is applied to temperature fields derived from Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) data on board the Venus Express spacecraft. We obtain a zonal thermal wind field that is in better agreement with other, more direct methods based on either retrieving the zonal winds from cloud tracking or from direct measurements of the meridional slope of pressure surfaces.     

Titan global climate model: A new 3-dimensional version of the IPSL Titan GCM

We have developed a new 3-dimensional climate model for Titan’s atmosphere, using the physics of the IPSL Titan 2-dimensional climate model with the current version of the LMDZ General Circulation Model dynamical core. Microphysics and photochemistry are still computed as zonal averages. This GCM covers altitudes from surface to 500 km altitude, with barotropic waves now being resolved and the diurnal cycle included. The boundary layer scheme has been changed, yielding a strong improvement in the tropospheric zonal wind profile modeled at Huygens descent position and season. The potential temperature profile is fairly consistent with Huygens observations in the lowest 10 km. The latitudinal profile of the near-surface temperature is close to observed values. The minimum of zonal wind observed by the Huygens probe just above the tropopause is also present in these simulations, and its origin is discussed by comparing solar heating and dynamical transport of energy. The stratospheric temperature and wind fields are consistent with our previous works. Compared to observations, the zonal wind peak is too weak (around 120 m/s) and too low (around 200 km). The temperature structures appear to be compressed in altitude, and depart strongly from observations in the upper stratosphere. These discrepancies are correlated, and most probably related to the altitude of the haze production. The model produces a detached haze layer located more than 150 km lower than observed by the Cassini instruments. This low production altitude is due to the current position of the GCM upper boundary. However, the temporal behaviour of the detached haze layer in the model may explain the seasonal differences observed between Cassini and Voyager 1. The waves present in the GCM are analyzed, together with their respective roles in the angular momentum budget. Though the role of the mean meridional circulation in momentum transport is similar to previous work, and the transport by barotropic waves is clearly seen in the stratosphere, a significant part of the transport at high latitudes is done all year long through low-frequency tropospheric waves that may be baroclinic waves.     

Maintenance of equatorial superrotation in the atmospheres of Venus and Titan

This paper extends Leovy's theory on Venus’ equatorial superrotation by analytically examining additional terms in the mean zonal momentum equation that stably balances the momentum source of pumping by thermal tides. The general analytical solution is applied to the atmospheres of both Venus and Saturn's moon Titan. The main results are: (i) Venus’ equatorial superrotation of 118 m s⁻¹ results primarily from a balance between the momentum source of pumping by thermal tides and the momentum sink of meridional advection of wind shear by horizontal branches of the Hadley circulation; (ii) no solution is found for Titan's stratospheric equatorial superrotation centered at the 1-hPa level; (iii) however, if the main solar radiation absorption layer in Titan's stratosphere is lifted from 1 hPa (∼185 km) to 0.1 hPa (∼288 km), an equatorial superrotation of ∼110 m s⁻¹ centered at 0.1-hPa could be maintained. Titan's equatorial superrotation results mainly from a balance between the momentum source of tidal pumping and the momentum sink of frictional drag.     

Superrotation of upper atmosphere by global deposition of meteoroids

A new theory of the superrotation of upper atmosphere is worked out on the basis of global deposition of meteoroids assuming that a certain constant influx of meteoroids is continually falling upon the Earth's atmosphere. On the average the meteoroids are shown to carry a greater amount of orbital angular momentum than that corresponding to the Earth's orbit about the Sun. It is argued that the excess of orbital angular momentum appears as extra spin angular momentum in the atmospheric layer in which the meteoroids are arrested and this is used to calculate the velocity difference which can be maintained across a certain layer of the atmosphere. It is found that a global deposition of 34 tons/day of meteoric material is required to account for the observed superrotation which agrees with the recent estimates on meteoric mass influx on the Earth.     

On a probable mechanism of superrotation of the atmosphere of venus

It is shown in the paper that the mechanism of superrotation of the atmosphere of Venus consists of several interrelated processes, including the transport of angular momentum from the solid planet to the atmosphere at a wind flow over the planet’s surface relief, the upward transport of momentum by threedimensional turbulent vortices, the inverse energy cascade in a large-scale quasi-two-dimensional flow, and the horizontal transfer of angular momentum in the Hadley cell. These processes make different contributions to the superrotation at different altitudes.     

The axial angular momentum of the general circulation of the oceans

With the Hamburg geostrophic ocean general circulation model, the temporal variation of the angular momentum of the oceans is studied. The input wind stresses consist of climatological winds plus the deviations of the actual winds 1981–1989. The motion part of the angular momenta of the two hemispheres resembles the (counter-phase) behaviour of the corresponding atmospheric angular momentum. The dominating matter part however shows no phase shift between the hemispheres. The sum of the angular momenta of the solid Earth and the atmosphere is deduced from observations; in principle it should be inversely correlated to the oceanic angular momentum. A first attempt to recognize the correlation between these empirical data and the theoretical values is described.