General circulation model simulations of superrotation in slowly rotating atmospheres: Implications for Venus

A series of experiments with a three dimensional general circulation model developed to simulate Earth's atmosphere is run with planetary rotation rates varying between 1 and 1/64 times Earth's rotation rate and diurnally averaged thermal forcing. Results are used to evaluate theories of Venus' atmospheric superrotation which invoke upward transport of angular momentum from the solid planet by the zonal mean (i.e., axisymmetric) circulation. The theories predict that superrotation is a common feature of slowly rotating planetary atmospheres, suggesting that superrotation should appear in the idealized slowly rotating cases of the present study. We find, however, that although dynamical mechanisms suggested for axisymmetric forcing of superrotation appear in model spinups from rest, the steady-state circulations include only weak globally averaged superrotation, consistent with previously reported results from lower resolution models. It appears that during spinup the thermally driven equator-to-pole circulation rapidly generates zonal-mean winds near the planetary surface which preclude vertical angular momentum transport and thus suppress further development of the superrotation. If this is the case, then the diurnally varying component of solar heating, such as atmospheric tides or the “moving flame”, must be included to explain Venus' strong atmospheric superrotation.     

Hydrodynamic Source of the 11-year Solar Variations

In the traditional axisymmetric models of the 11-year solar cycle, oscillations of the magnetic fields appear in the background of nonoscillating (over time scale considered) turbulent velocity fields and differential rotation. In this paper, an alternative approach is developed: The excitation of magnetic oscillations with the 22-year period is the consequence of hydrodynamic oscillations with the 11-year period. In the excitation of hydrodynamic oscillations, two processes taking place in high latitudes near the interface between the convective and radiative zones play a key role. One is forcing of the westerly zonal flow, the conditions for which are due to deformation of the interfacial surface. The other process is the excitation of a shear instability of zonal flow as a consequence of a strong radial gradient of angular velocity. The development of a shear instability at some stage brings about the disruption of the forcing of differential rotation. In the first (hydrodynamic) part of the paper, the dynamics of axisymmetric flows near the bottom of the convection zone is numerically simulated. Forcing of differential rotation having velocity shear in latitude and the existence of solutions in the form of torsional waves with the 11-year oscillation period are shown. In the second part the dynamics of the magnetic field is studied. The most pronounced peculiarities of the solutions are the existence of forced oscillations with the 22-year period and the drift of the toroidal magnetic field component from the mid latitudes to the equator. In high and low latitudes after cycle maximum, the toroidal component is of opposite sign in accordance with observations. In the third part, the transport of momentum from the bottom of the convection zone to the outer surface by virtue of diffusivity is considered. The existence of some sources of differential rotation in the convection zone is not implied. A qualitative correspondence of the differential rotation profile in the bulk of the convection zone and on its outer surface to experimental data is shown. The time correspondence between torsional and magnetic oscillations is also in accordance with observations.     

An analysis of the strong zonal circulation within the stratosphere of Venus

A dynamical model is presented for the observed strong zonal circulation within the stratosphere of Venus. The model neglects rotational effects and considers a compressible and radiating atmosphere. It is shown that diurnal radiative heating is negligible within the lower stratosphere, a region below 85km, while observational evidence for the strong zonal circulation pertains to the lower stratosphere within which a direct thermal driving for the circulation is absent. The analysis, however, suggests that propagating internal gravity waves generated by diurnal solar heating of the upper stratosphere induce mean zonal velocities within the upper and lower stratosphere.Considering the linearized equations of motion and energy, and following Stern's (1971) analysis for an analogous problem, it is shown that the zonal velocity induced by internal gravity waves is retrograde in direction, a result which is in agreement with observation. The nonlinear equations of motion and energy are then solved by an approximate analytical method to determine the magnitude of the zonal velocity. This velocity increases from zero at the tropopause to about 200 msec^?1 at the 85 km level. The velocity near the uv-cloud level compares favorably with the observed value of 100 msec^?1.     

Venus' superrotation,mixing length theory and eddy diffusion: A parametric study

The Hadley mechanism is adopted to describe the axisymmetric four day superrotation in the Venus atmosphere, with solar driven meridional winds redistributing energy and momentum, and eddy diffusion describing the actions of three dimensional transient eddies. We address the question how the eddy diffusion coefficients are related to the properties of the circulation. For the atmosphere of a slowly rotating planet such as Venus, we show that a form of the non-linear closure is suggested by the mixing length hypothesis, which constrains the magnitude of the eddy diffusion coefficients. Combining this constraint with the concept of the Rossby radius of deformation yields zonal velocities on the order of 100 m sec^–1. A steady state, non-linear, one-layer spectral model is used for a parametric study to find a relationship between heat source, meridional circulation and eddy diffusion coefficients, which yields the large zonal velocities observed. This analysis leads to the following conclusions: (1) Proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. (2) The meridional velocity is virtually constant for large eddy diffusion coefficients. (3) Below a threshold in the diffusion rate, the meridional velocity decreases, commensurate with the mixing length hypothesis. Eddy heat conduction becomes important and shares with the Hadley cell advection in balancing the solar heating. The zonal velocities then reach large values near 100 m sec^–1. (4) For large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates. However, under condition (3), the zonal velocities are independent of the planetary rotation rate. Ramifications are discussed for related parameterizations in GCMs, emphasizing that eddy diffusion coefficients are governed by solar forcing and cannot be chosen independently.     

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.     

Influence of Ohmic diffusion on the excitation and dynamics of MRI

In this paper we make an effort to understand the interaction of turbulence generated by the magnetorotational instability (MRI) with turbulence from other sources, such as supernova explosions (SNe) in galactic disks. First we perform a linear stability analysis (LSA) of non‐ideal MRI to derive the limiting value of Ohmic diffusion that is needed to inhibit the growth of the instability for different types of rotation laws. With the help of a simple analytical expression derived under first‐order smoothing approximation (FOSA), an estimate of the limiting turbulence level and hence the turbulent diffusion needed to damp the MRI is derived. Secondly, we perform numerical simulations in local cubes of isothermal nonstratified gas with external forcing of varying strength to see whether the linear result holds for more complex systems. Purely hydrodynamic calculations with forcing, rotation and shear are made for reference purposes, and as expected, non‐zero Reynolds stresses are found. In the magnetohydrodynamic calculations, therefore, the total stresses generated are a sum of the forcing and MRI contributions. To separate these contributions, we perform reference runs with MRI‐stable shear profiles (angular velocity increasing outwards), which suggest that the MRI‐generated stresses indeed become strongly suppressed as function of the forcing. The Maxwell to Reynolds stress ratio is observed to decrease by an order of magnitude as the turbulence level due to external forcing exceeds the predicted limiting value, which we interpret as a sign of MRI suppression. Finally, we apply these results to estimate the limiting radius inside of which the SN activity can suppress the MRI, arriving at a value of 14 kpc (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Venusian middle-atmospheric dynamics in the presence of a strong planetary-scale 5.5-day wave

The middle atmospheric dynamics on Venus are investigated using a middle atmosphere general circulation model. The magnitude of the superrotation is sensitive to the amplitude of the planetary-scale waves. In particular, the critical level absorptions of the forced planetary-scale waves might contribute to the maintenance of the superrotation near the cloud base. In the case of strong 5.5-day wave forcing, the superrotation with zonal wind speed higher than 100 m s^?1 is maintained by the forced wave. Four-day and 5.5-day waves are found near the equatorial cloud top and base, respectively. The planetary-scale waves have a Y-shaped pattern maintained by the amplitude modulation in the presence of strong thermal tides.The polar hot dipole is unstable and its dynamical behavior is complex near the cloud top in this model. The dipole merges into a monopole or breaks up into a tripole when the divergent eddies with high zonal wavenumbers are predominant in the hot dipole region. A cold collar is partly enhanced by a cold phase of slowly propagating waves with zonal wavenumber 1. Although such a complex dipole behavior has not been observed yet, it is likely to occur under a dynamical condition similar to the present simulation. Thus, the dynamical approach using a general circulation model might be useful for analyzing Venus Express and ground-based observation data.     

Instability of Zonal Flows in Rotating Spherical Shells: An Application to Jupiter

Measurements from the Galileo probe suggest that the zonal winds are deep rooted. Jupiter's high rotation rate makes it likely that the whole outer molecular H/He layer is involved in these long-lived jet flows. Assuming that the primary flows are geostrophic, and that the banded surface structure stretches right through the molecular H/He layer, we examine the conditions for such flows to be stable. As a first step, the linear stability of some prescribed banded zonal flows in a rotating spherical shell is explored. Incompressibility is assumed for simplicity, and the boundary condition is stress-free. We compare solutions for two aspect ratios, appropriate for the molecular H/He layers of Jupiter and Saturn, and two Ekman numbers (E=10⁻² and E=10⁻⁴). Convective and shear flow instabilities compete in our system. The convective instabilities are of the well-known columnar structure. Shear flow instabilities for the larger Ekman number are similar to the Taylor-Couette instability in rotating annuli. At the lower Ekman number, shear flow instabilities adopt a geostrophic character, assuming the form of rotating columns, similar to the convective instabilities. While the convective instability always sets in outside the tangent cylinder, shear instability can become unstable inside the tangent cylinder. If even a weak zonal flow is present inside the tangent cylinder, the flow is unstable to shear instability. This offers an explanation why the jovian zonal jet structure is much weaker at the higher latitudes that correspond to locations inside the tangent cylinder.     

Exchange of global mean angular momentum between an atmosphere and its underlying planet

This paper investigates the exchange of global mean angular momentum between an atmosphere and its underlying planet by a simple model. The model parameterizes four processes that are responsible for zonal mean momentum budget in the atmospheric boundary layer for a rotating planet: (i) meridional circulation that redistributes the relative angular momentum, (ii) horizontal diffusion that smoothes the prograde and retrograde winds, (iii) frictional drag that exchanges atmospheric angular momentum with the underlying planet, and (iv) internal redistribution of the zonal mean momentum by wave drag. It is shown that under a steady-state or a long-term average condition, the global relative angular momentum in the boundary layer vanishes unless there exists a preferred frictional drag for either the prograde or the retrograde zonal wind. We further show quantitatively that one cannot have either a predominant steady prograde or retrograde wind in the boundary layer of a planetary atmosphere. The parameter dependencies of the global relative angular momentum and the strength of the atmospheric circulation in the boundary layer are derived explicitly and used to explain the observational differences between the atmospheres of Earth and Venus.     

Modeling Jupiter's cloud bands and decks: 1. Jet scale meridional circulations

We have investigated the formation of jet scale meridional circulation cells on Jupiter in response to radiative and zonal momentum forcing. In the framework of semi-geostrophic theory, the meridional streamfunction is described by an elliptic equation with a source term dependent on the sum of the latitudinal derivative of the radiative forcing and the vertical derivative of the zonal momentum forcing. Using this equation with analytic terms similar to the assumed forcing on Jupiter, we obtained two set of atmospheric circulations cells, a stratospheric and a tropospheric one. A possible shift in the overturning circulation of the high and deep atmosphere can be induced by breaking the latitudinal alignment of radiative heating with the enforced belt and zones. A series of numerical simulations was conducted with the Jovian GCM OPUS, which was initiated with observational data obtained from the Cassini CIRS temperature cross-section and a corresponding geostrophic zonal wind field. Newtonian forcing of potential temperature as well as zonal momentum was applied respectively towards latitudinally and vertically uniform equilibrium fields. In accordance with the analytic illustrations two rows of jet scale circulation cells were created. The stratospheric circulation showed the distribution of upwelling over zones and downwelling over belts, consistent with cloud observations. The tropospheric cells featured a partial reversal of the downward vertical velocity over the belts and a considerable reduction of the upward movement over the zones in the domain, consistent with recent detections of high water clouds and lightning in belts. We also used the modeled new forcing fields as source terms for the semi-geostrophic Poisson equation to attribute the origin of the modeled secondary circulation. In this analysis, the stratospheric circulation cells observed in the model are primarily generated in response to radiative forcing, while momentum forcing induces the shifted configurations in the deep atmosphere.     

Large-scale flows excited by magnetic fields in the solar convective zone

Observations demonstrate a nearly 22-year periodic zonal flow superimposed on general solar differential rotation (LaBonte and Howard, 1982) and some meridional motions (e.g., Tuominen, Tuominen, and Kyrolänen, 1983). Such flows can be excited by the magnetic wave generated by the dynamo in the solar convective zone.An approximate analytical solution for the zonal and meridional flows for a given magnetic wave is constructed. This approach is justified by the fact that the magnetic field is generated by differential rotation and mean helicity, and the magnetic field in the time interval under consideration does not affect much this main flow; it can, however, strongly influence the perturbations of this flow.The density gradient in the convective zone is taken into account as an essential point in the solution construction. The solution agreed well with observational features and, in particular, it gives a phase shift between the rotational (zonal) wave and solar activity. A polar branch of the rotational wave can be described as an effect created by a poleward moving dynamo wave.Secular variations in the symmetrical part of the differential rotation and in the asymmetry between the north and south hemispheres are predicted.The alternative approaches to the explanation of the origin of the observed large-scale flows are discussed.     

The frequency composition of the Madden-Julian oscillation. An indication of the solar activity contribution to the global atmospheric circulation and the Earth's rotation

In the series of the solar activity indices, the zonal component of the atmospheric momentum (AAM), and the Earth rotation variations (UT1-TAI), power spectra concentrations at 40, 50, and 60–80 day period are detected. This result indicates the solar origin of the Madden-Julian oscillation in atmospheric circulation and the 50-day oscillation of the Earth's rotation.     

On a physical mechanism for extra mixing in globular cluster red giants

For the first time we propose a real physical mechanism for 'extra mixing' in red giants that can quantitatively interpret all the known star-to-star abundance variations in globular clusters. This is Zahn's mechanism. It considers extra mixing in a radiative zone of a rotating star as a result of the joint operation of meridional circulation and turbulent diffusion. It is shown that the only free parameter, the angular velocity at the base of the convective envelope, can be so adjusted as to fit the observed abundance correlations without leading to a conflict with available data on rotation velocities of blue horizontal branch stars in the same cluster. There are two critical assumptions in our model, that the top of the radiative zone is not in synchronous rotation with the stellar surface but rotates significantly faster and that the criterion for shear instability takes a particular form. These will eventually be tested by three-dimensional hydrodynamical simulations.     

Zonal winds near Venus' cloud top level: An analytic model of the equatorial wind speed

It is proposed that the equatorial wind speed near Venus' cloud top level is maintained by a balance between the pumping effect of the semidiurnal tide and vertical advection by the Hadley circulation, both integrated across the thermal driving region. A consequence of this hypothesis is that the maximum equatorial zonal wind speed is proportional to Nh where N is buoyancy frequency and h is a measure of the thickness of the driving region. The proportionality constant is a weakly increasing function of the heating rate and a decreasing function of λh, where λ is an inverse length characterizing the mean zonal wind shear. The equilibrium solution considered is shown to be stable. For the class of solutions investigated, there is a threshold value of heating rate below which there is no equilibrium satisfying the hypothesized balance, but this result depends on the assumption that the shape of the zonal wind profile is invariant with thermal forcing amplitude.     

Large-scale zonal flow and magnetic field generation due to drift-Alfven turbulence in ionosphere plasma

In the present work, the generation of large-scale zonal flows and magnetic field by short-scale collision-less electron skin depth order drift-Alfven turbulence in the ionosphere is investigated. The self-consistent system of two model nonlinear equations, describing the dynamics of wave structures with characteristic scales till to the skin value, is obtained. Evolution equations for the shear flows and the magnetic field is obtained by means of the averaging of model equations for the fast-high-frequency and small-scale fluctuations. It is shown that the large-scale disturbances of plasma motion and magnetic field are spontaneously generated by small-scale drift-Alfven wave turbulence through the nonlinear action of the stresses of Reynolds and Maxwell. Positive feedback in the system is achieved via modulation of the skin size drift-Alfven waves by the large-scale zonal flow and/or by the excited large-scale magnetic field. As a result, the propagation of small-scale wave packets in the ionospheric medium is accompanied by low-frequency, long-wave disturbances generated by parametric instability. Two regimes of this instability, resonance kinetic and hydrodynamic ones, are studied. The increments of the corresponding instabilities are also found. The conditions for the instability development and possibility of the generation of large-scale structures are determined. The nonlinear increment of this interaction substantially depends on the wave vector of Alfven pumping and on the characteristic scale of the generated zonal structures. This means that the instability pumps the energy of primarily small-scale Alfven waves into that of the large-scale zonal structures which is typical for an inverse turbulent cascade. The increment of energy pumping into the large-scale region noticeably depends also on the width of the pumping wave spectrum and with an increase of the width of the initial wave spectrum the instability can be suppressed. It is assumed that the investigated mechanism can refer directly to the generation of mean flow in the atmosphere of the rotating planets and the magnetized plasma.     

The Kelvin-Helmholtz instability in the low-latitude boundary layer

The Kelvin-Helmholtz instability on the magnetopause has frequently been invoked as a mechanism for driving geomagnetic pulsations in the Pc3–Pc5 range, as well as to explain the occurrence of surface waves on the magnetopause observed by satellites. Most theories of the instability represent the magnetopause by a sharp boundary with velocity shear. In this paper a linear theory is developed which takes into account the finite thickness of the low-latitude boundary layer on the magnetopause. The theory is in a form suitable for numerical computation and can take into account the effect of gradients in the plasma pressure, magnetic field magnitude and direction, and density. Computations show that the instability is suppressed at wavelengths short compared with the scale width of the boundary. There is thus a wavelength for which the growth rate is maximum. Extensive computations have been carried out and they show that growth can take place for a very wide range of conditions. The computations confirm earlier results snowing that maximum growth occurs for a wave vector which is perpendicular to the magnetic field. For typical solar wind conditions the theory predicts wavelengths on the magnetopause of the order of 10 times the thickness of the low-latitude boundary layer and periods in the Pc3–Pc5 range. The possible non-linear development of the instability is discussed qualitatively. The predicted results are consistent with satellite observations of pulsations.     

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.     

Zonal mean circulation at the cloud level on Venus: Spring and fall 1979 OCPP observations

Cloud motions were obtained from a number of images acquired in reflected solar ultraviolet light during spring and fall of 1979 from the Pioneer Venus Orbiter Cloud Photopolarimeter (OCPP) to determine the zonal mean circulation of the atmosphere of Venus at the cloud top level. The meridional profile of the zonal component of motion is somewhat different from that previously obtained from Mariner 10 and preliminary Pioneer Venus observations, although the equatorial magnitude is about the same (?94 m/sec). The mean meridional motion is toward the south pole south of about 5° south latitude, and toward the north pole north of this latitude, with peak mean magnitudes of about 7 m/sec polewards of 20° north and 40° south latitudes in the respective hemispheres. From the few measurements obtained at higher latitudes the magnitude of the mean meridional component appears to decrease although it is still directed toward the respective poles. Due to the evolution of the cloud patterns over the duration of the images from which the cloud velocities are obtained, the uncertainties in the mean zonal and meridional components may be as large as 5–10 and 2–4 m/sec, respectively. Preliminary estimates of meridional momentum transport show that the mean circulation dominates the eddy circulation transport completely, in agreement with the estimates obtained from Mariner 10 data, although the uncertainties in both the mean and eddy circulation transports are large. The momentum transports are polewards and their peak magnitudes occur at latitudes between 20° and 40° in both the hemispheres.     

A reanalysis of Venus winds at two cloud levels from Galileo SSI images

The global circulation of the Venus atmosphere is characterized at cloud level by a zonal super rotation studied over the years with data from a battery of spacecrafts: orbiters, balloons and probes. Among them, the Galileo spacecraft monitored the Venus atmosphere in a flyby in February 1990 in its route toward Jupiter. Since the flyby was almost equatorial, published analysis of zonal winds obtained from displacements of cloud elements on images obtained by the SSI camera [Belton, M.J.S., and 20 colleagues, 1991. Science 253, 1531-1536] stop at latitudes 50° north and south. In this paper we present new results on Venus winds based on a reanalysis of an extended set of images obtained at two wavelengths, 418 nm (violet) and 986 nm (near infrared), that sense different altitude levels in the upper cloud. Our main result is that we have been able to extend the zonal wind profile up to the polar latitudes: 70° N and 70° S at 418 nm and 70° N at 986 nm. Binned and smoothed profiles are given in tabular form. We show that the zonal winds drop in their velocity poleward of latitudes 45° N and 50° S where an intense meridional wind shear develops at the two cloud levels. Our data confirm the magnitude of this shear, retrieved previously from radio occultation data, but disagrees with it in the latitudinal location of the sheared region. The new wind data can be used to recalibrate the zonal winds retrieved from the previous measurements of the temperature field and the cyclostrophic balance assumption. The meridional profiles of the zonal winds at the two cloud levels are used to assess the vertical wind shear in the upper cloud layer as a function of latitude and locate the most unstable region.     

Zonal winds near Venus' cloud top level: A model study of the interaction between the zonal mean circulation and the semidiurnal tide

A primitive equation wave-mean flow interaction model, designed by J. R. Holton and used originally to study Earth's middle atmosphere, has been adapted to Venus in order to clarify our understanding of the interaction between the semidiurnal tide and the thermally driven mean meridional circulation near the cloud top level. With or without the tide the model produces midlatitude jets whose structure is insensitive to vertical shear of the background angular velocity above and below the cloud top level, but it is sensitive to background angular velocity at the cloud top level. When this background angular velocity is close to that of Venus, the latitudes and speeds of these jets are similar to the latitudes and speeds of jets at the Venus cloud top level as inferred from observed temperatures and the cyclostrophic balance condition. In agreement with the hypothesis of Fels and Lindzen, the model tide accelerates the equatorial zonal wind near the cloud top level and decelerates it at higher levels. The tidal vertical wavelength, maximum amplitude, dissipative decay length, and zonal flow accelerations are sensitive functions of background angular velocity, in agreement with elementary gravity wave theory. In the equatorial cloud top region, tidal acceleration is comparable in magnitude to the decelerative effects of vertical advection and the model's Rayleigh friction damping. For sufficiently rapid initial zonal flow near the cloud top level, the area-weighted global mean cloud top level zonal wind increases with time over a 50-day model run as a result of tidal acceleration. Agreement between the model tide and the observed tide, or the tide determined in the more detailed calculations of Pechmann and Ingersoll, is best when the background angular velocity at the jet level is about 30% larger than that observed.