JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. E3, PAGES , MARCH 25, balance of the Venusian midlatitude

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. E3, PAGES , MARCH 25, 1997 Momentum mesosphere balance of the Venusian midlatitude Takeshi hnamur Department of Earth and Planetary Physics, Graduate School of Science, University of Tokyo Tokyo. Japan Abstract. The downward control principle is applied to estimate the vertically integrated zonal force driving the midlatitude lower mesosphere on Venus. The distinct localization of the forcing in the midlatitude implies two candidates for the momentum carrier: Rossby wave; and internal gravity waves generated by shear inst, ability. Rough estimates of the Eliassen-Palm (EP) flux suggesthat the meridional circulation will be driven principally by the EP flux divergence associated with a Rossby wave, although the contribution of gravity waves cannot be ruled out. It is also shown that advective transport is as important as eddy diffusion for tracer transport. 1. Introduction In the Venusian mesosphere (60-90 kin) the polar regions are warmer than the tropics [Schubert et al., 1980]. The radiative equilibrium model by Crisp [1989] shows that the model mesospheric temperatures are up to 60øK cooler in the polar region and 10øK warmer in the equatorial region than observations. A possible mechanism to maintain the reversed temperature gra- advection. 2. Zonal Force Requirement Baker and Leo'vy [1987] have introduced zonal forces into their numerical model in the form of Rayleigh We consider a steady and zonally averaged atlllofriction, and reproduced subsidence and compressional sphere and use the transformed Eulerian-mean (TEM) heating in polar regions. The diagnostic analysis by equations [Andrews and Mcintyre, 1978]. Combining Hou and Goody [1989] suggests momentum sources oc- the zonal momentum equation with the mass continucur at nfidlatitudes, since the air moves horizontally ity equation and requiring that P0 * across the midlatitude where angular momentum changes we have abruptly. Eddy diffusivity cannot transport momentum 1 0 enough to maintain the momentum balancexcept in p0 *= the turbuhmt layer around the cloud base (50-55 kin), as a cos ½ 0½ cos O f p0 ( _ 0a _, shown later. The semidiurnal tides, which may be important for the maintenance of the superrotation [Fels and Lindzen, 1974; Newman and Leovy, 1992], have lit- where tle influence on the mean zonal flow at middle and high q = 2f2 sin ½ 1 O(acosqb) (2) latitudes [Baker and Leovy, 1987; Hou et al., 1990]; acos 0 therefore other mechanisms transferring momentum at is the absolute vorticity, z is the log-pressure height, midlatitudes are required. This paper shows that the b is the latitude,, is the zonal velocity (eastward is positive), * is the vertical component of the mean circulation, P0 is the density proportional to exp(-z/h), Copyright, 1997 by the American Geophysical Union. Paper number 96JE /97/96JE candidates are an upward propagating Rossby wave and internal gravity waves, which are expected to exist in the Venusian mesosphere. In section 2 we roughly estimate the forces acting on the zonal flow above clouds by applying the downward control principle [Haynes and Mcintyre, 1987; Mcintyre, 1989; Haynes et al., 1991]. The latitudinal distri- bution of the forcing severely constrains the mechanisms transferring momentum to drive the circulation. In secdient is a global-scale meridional circulation [Taylor et tions 3 and 4 we examine the contributions of an upal., 1983]' ascent in the equatorial region, poleward ad- ward propagating midlatitude Rossby wave and internal vection above clouds, subsidence in the polar region and gravity waves. In section 5 we discuss the implication of equatorward advection below clouds. If such a circula- the circulation for constituent transport and conclude tion exists, then the conservation of angular momen- that the concept of a "wave-driven extratropical pump" tum at each latitude requires deceleration/acceleration is valid also in the VenusJan mesosphere. acting on the zonal flow in the poleward/equatorward 6615 H is the mean density scale height, f2 is the planetary -- rotation rate, a is the planetary radius and G is the zonal force per unit mass due to Rossby and gravity

2 _ 6616 IMAMURA: MOMENTUM BALANCE OF VENUSIAN MESOSPHERE vave breakings and other dissipative eddy processes. Equation (1) is similar to equation (2.6) of Haynes et al. [1991] and shows the downward control of the vertical mass flux by zonal forces [Haynes and Mcintyre, 1987; Mcintyre, 1989]. The downward control nature is evident in the results of the diagnostic analysis by Hou and Goody [1989], although they have not mentioned the principle explicitly. Here we replace r/(, z/) in the integral with q(, Zc), where Zc is the cloud top level. The validity of the replacement for r/is examined in the _ last section. Allowing that G = 0 and Oa/Oz - 0 at - 7r/2, we have the zonal forces vertically integrated above clouds, ' = Po U dz' t * qpoa coso cos ;b'd6' +/ Po ff dz, (3) where t * is related to the departure of temperature from radiative equilibrium, 5 ', as i '04 1 ' 0.02 o.o G latitude (degree) loo. ' Figure 1. Latitudinal distributions of westward wind speed - i (dot-dashed curve) and the departure of temperaturc from radiative equilibrium 5T (dotted curve) at the cloud top level used for the calculation, and the calculated zonal force vertically integrated above clouds (bold solid curve). * " - T (4) - N2H lnagnitude. The candidates are a midlatitude Rossby wave and internal gravity waves, which are expected xvhere N is the buoyancy frequency, c is the radiative to transfer lnomentuln upward from the cloud level to relaxation rate and / is the gas constant. Given the the mesosphere. The vertical momentum diffusion by meridional distributions of and 5f, (3) and (4) enable small-scale eddies will make a minor contribution above us to calculate C. clouds: using a by Newman et al. [1984] and the eddy The distribution of above clouds has been dediffusion coefficient by Woo and Ishimaru [1981] yields rived from temperature measurements assuming cy- the diffusive momentum flux smaller than N m -2. clostrophic balance by $ei et al. [1980] and Newman et The atmospheric tides will also make a minor contribual. [1984], but their winds derived at the cloud top level tion: theoretical estimates of the Eliassen-Palm (EP) (,,65 km altitude) are larger than the cloud-tracked flux divergence due to tides [Fels, 1986; Baker and winds [Rossow et al., 1980]. Rough estimates using Leovy, 1987; Hou et al., 1990; Newman and Leovy, 1992] given by Ncwman et al. have shown that the neglection yield the vertically integrated force above clouds to be of the second term on the right-hand side of (3) does less than N m -2 at all latitudes. not change the latitudinal distribution of 6 significantly (less than 0.01 N m-2). For these reasons we consider only the first term on the right-hand side of (3), then is calculated using the values at the cloud top level 3. Midlatitude Rossby Wave only. 5 and a are given by Crisp [1989], and other atmospheric parameters are taken from 5'ei et al. [1985] and Schubert and Walterscheid [1984]. Figure 1 shows the latitudinal distributions of and 6 used for the calculation and the calculated 6 for z = 65 kin. The distribution of a roughly represents _ the cloud-tracked winds, and that of 5T satisfies the equation /2 oso do -0 (5) A planetary-scale midlatitude wave with zonal wave nmnber 1 has been identified in Pioneer Venus cloud- tracked winds at the cloud top level by Del Genio and _Rossow [1990] and Rossow et al. [1990]. Their analysis shows the wave has the period of,,5 days and the Doppler-shifted phase speed c-,,, 32 m s -1. They have suggested the 5-day wave has the characteristics of a vertically propagating midlatitude Rossby wave and that its amplitude is large enough to affect the momen- tran balance. The existence of the wave above clouds is evident from the Pioneer Venus orbiter infrared ra- so that the net vertical mass flux across the cloud top level equals zero. has its maximum in the midlatitude diometer data: Taylor et al. [1980] and Apt and Leung [1982] report 5.5-day and 5.3-day periodicities, respecas a result of the horizontal motions across the midlat- tively, in the midlatitude brightness temperature. Tayitude where angular momentum changes abruptly; this lor et al. [1980] suggested the vertical propagation of is qualitatively consistent with Hou and Goody [1989J. the wave with a vertical phase velocity of the order 4 The magnitude of at midlatitudes is N m -z cm s -1. The decrease of the amplitude from the cloud The mechanisms responsible for the forces must satisfy both the midlatitude localization and the estimated top to the 80-km altitude [Apt and Leung, 1982] implies the EP flux divergence at km altitudes.

3 IMAMURA: MOMENTUM BALANCE OF VENUSIAN MESOSPHERE 6617 The source of the 5-day wave is unclear. Barotropic instability of the zonal flow, which is forced by the meridional circulation, is a likely mechanism for producing eddies. The analysis of UV images suggests the occurrence of barotropic eddy disturbances at midlatitudes [Travis. 1978]. In the mature stage of the disturbance a nonlinear cascade of energy to larger eddies will produce a Rossby wave having a zonal wavenumber 1 [Rossow and Williams, 1979]. A portion of the required zonal force may be explained by the equatorward momentum transport by barotropic eddies, which might be important for the maintenance of the superrotation [ Gierasch, 197.5]. Now we roughly estimate the EP flux associated with the Rossby wave at the cloud top level using a linear theory on a midlatitude /3 plane [e.g., Andrews et al, 1987]. The vertical component of the EP flux, F, is given by where r xp0j;-mli, le,(6) /3 k 2 1 ',n_ e(a- c) e 4H 2, (7) montet al., 1986; $eiff and Kirk, 1991; Hinson and Jenkins, 1995], and some of them may be attributed to internal gravity waves. The activity of gravity waves generated by topography [Young et al., 1994] or convection [Hou and Farrell, 1987] at the ground surface is unlikely to localize in the midlatitude, since equatorial regions have larger topography than midlatitudes and observations show greater penetration of sunlight at small solar zenith angle [Tomasko, 1983], but the latitudinal difference of wave dissipation below clouds might explain the midlatitude localization. The distribution of the waves generated by the convection at the cloud base is uncertain since the convective activity depends on the heat transport in the lower atmosphere [Leroy and Ingersoll, 1996]. Hinson and Jenkins [19951 derived the characteristics of a gravity wave from the Magellan radio occultat, ion temperature measurements, but. the estimated wave amplitudes yield the vertical EP flux of N m -2, which is much smaller than the required forces at midlatitudes. Generation of gravity waves by shear (KH) instability at the cloud base will be localized in the midlatitude, where convective disturbances will be weak and wind shear is large. The wind shear is expected to be maine - f /N 2, fo - 20* sin d0 is the Coriolis param- tained by the meridional circulation as a consequence of eter at. latitude. ½0, /2* is the angular velocity for a the latitudinal gradient of angular momentum: above coordinate system rotating with the local wind at 0, clouds there will be poleward advection of air having k - (a cos 00) - is the zonal wavenumber, m is the ver- large angular momentum, while below clouds there will tical wavenumber, fi is the absolute vorticity gradient be equatorward advection of air having small angular and is the amplitude of stream hnction. momentum. Around the cloud base, where the atmo- The key parameter for the F evaluation is the amplitude of the observed 5-day wave. The zonal wind distribution assumed for the evmuat, ion (see Figure 1) sphere is close to neutral static stability due to solar heating, the Richardson number falls short of 0.25 which is the critical value for the initiation of shear instability. is similar to the time-averaged values observed in 1979 Radar observations have revealed that the excitation and 1985, in which the contrast of midlatitude jets was sources of short-period gravity waves in the terrestrial decreased [Rossow et al., 1990]. During those periods stratosphere are located near the jet stream [Murayama the lower limits of the meridionm wind amplitude at et ed., 199d] in which unstable shear layers will gener ø latitudes ranged from 6 to 8 m s- [Rossow et ate gravity waves [e.g., Sutherland and Peltier, 1994]: al., 1990]. We adoptentatively the vmue of 8 m s- as it would be reasonable to expect the same mechanism the typical amplitude at ½0-45 ø, where peaks. to work on Venus. Taking ß - (8 m s- )/k, c- a - 32 m s - O* = -2 (3.47 day) -1 and m -1 s - at ½0-45 ø 4.2. Generation by Shear Instability [Del Genio and Rossow, 1990], and N- 2x10-2 s - Since the spatial structure of the disturbance arisand H- 5 km as characteristic values at midlatitudes, ing from shear instability has never been observed on we obtmn the EP flux at the cloud top level to be F Venus, we seek to know the fastest growing mode by lin N m -2 with the vertical wavelength of 22 kin. ear instability analysis. We adopt the equation given by The vertical phase speed is estimated to be 5 cm s -1, Chimonas [1970] governing the spatial/temporal strucbeing roughly consistent with the observational result ture of infinitesimal perturbations in a two-dimensional by Taylor et al. [1980]. The estimated EP flux compressible fluid. The equation and boundary condi- N m -2 is the same order of magnitude as the required tions form an eigenvalue problem, and the problem is forces at midlatitudes, N m -2 (see Figure 1). solved iteratively using the method of Davis and Peltier Considering the uncertainties arising from some simpli- [1976]. The boundary conditions adopted are zero vefications, the EP flux associated with the midlatitude locity at the ground and radiation condition at the up- Rossby wave seems to explmn the driving forces of the circulation fairly well. per boundary. The background, and N are taken from Schubert 4. Internal Gravity Waves and Walterscheid [1984] as shown on the left panel of Figure 2, but a is modified above - 90 km for the sim Possible Sources plicity of the upper boundary condition. The vertical Small-scale wavelike structures have been observed structure of the fastest growing mode' is shown on the in the VenusJan atmosphere [Rossow et al., 1980; Bla- right panel of Figure 2. The KH disturbance at 50-56

4 ß 6618 IMAMURA' MOMENTUM BALANCE OF VENUSIAN MESOSPHERE buoyancy frequency (s- ) , 80 (,..., Re ':.i estimated lm(w). EP flux will be too small to account for the required forces N m -. Though the fastest growing mode cannot sustain waves with enough strength, the unstable shear layer will generate waves more effectively by increasing the horizontal scale of the disturbance through vortex pairing [Davis and Peltlet. 1979] or upscale scattering [Fritts, 1982; Chimonas and Grant, 1984]. For example, if horizontal wavelength were doubled, the EP flux would be F N m -2. Thus we cannot rule out the contribution of gravity waves because of the lack of knowledge on the nonlinear evolution of disturbances in the actual Venusian atmosphere zonal wind speed (ms' ) I I I I vertical velocity (arbitrary unit) Figure 2. (left,) Background zonal wind velocity a (dotted curve) and buoyancy frequency N (solid curve) used for shear instability analysis. (right) Structure of perturbation vertical velocity w associated with the fastest growing mode of shear instability. Dotted curve is for the real part, and solid curve is for the imaginary part. km altitudes generates a vertically trapped gravity wave at km because er > N, where er is the Dopplershifted frequency, while above 70 km a vertically propagating gravity wave is generated because er < N. The horizontal wavelength is -o10 km, the e-folding time of growth is,07 hours, and the horizontal phase speed is -070 m s -1, which is the fluid velocity at the cloud base. The horizontal wavelength is too short to be observed by the Pioneer Venus ultraviolet imager, whose spatial resolution is -030 km [Rossow et al., 1980]. The gravity wave will deposit momentum near critical level through convective breakdown or shear instability, since their dissipation through radiative relaxation or molecular viscosity is negligible [Imamura and Ogawa, 1995]. Let us consider a hypothetical situation where the disturbance on the unstable shear layer at the cloud base has reached a constant amplitude and formed vortex billows in its mature stage. Then a sustained generation of gravity waves from the layer will occur because the response in the upper fluid is the same as that of an inviscid flow over a wavy boundary [Mcintyre and Weissman, 1978]. Since a linear theory cannot predict amplitude, we tentatively adopt the vertical wind amplitude of 1.5 m s-ljust above the cloud base (56.5 kin), being consistent with the typical vertical velocity of VEGA balloon results [Blamont et al., 1986]. Then the vertical component of the EP flux at the cloud top level is calculated to be F,, 0.01 N m -. Considering that the sporadic nature of shear instability reduces the effective EP flux averaged over a long period, the 5. Discussion and Summary The replacement for /in the second section is valid insofar as the zonal force is confined to the altitude region where the zonal wind does not differ significantly from the cloud level wind. Such a condition is satisfied for the EP flux divergences by the Rossby and gravity waves discussed earlier because the waves are confined below the critical levels where the wind speed is equal to their horizontal phase speeds of m s -1. The maximum error of the evaluation arising from the replacement is an overestimation of -030%. The clmracteristic time of advective exchange for parcels in the Venusian mesosphere (here we take z > 65 kin) is defined as r t - A/I/, where A/I is the total mesospheric air mass and is the vertical mass flux across the 65 km altitude surface in the ascent region at lower latitudes. Using the parameters given earlier, the advective exchange time is calculated to be ra,, 90 days. On the other hand, the characteristic time of vertical diffusion is defined as rz> - H2/K, where K is the vertical eddy diffusion coefficient. Using the value K- 4 m 2 s -1 at -060 km altitude [Woo and Ishimaru, Pole.,' " wave-driven x X midlatitude pump : Rossby or gravity waves small scale eddies "'- ß ß.. :.' :.i:i.i: Equator Figure 3. Dynamical aspects of meridional circulation at the Venusian cloud level. Angular momentum advection associated with meridional circulation is canceled by the EP flux divergences associated with Rossby or gravity waves above the cloud base and small-scale eddies due to shear instability around the cloud base.

5 IMAMURA: MOMENTUM BALANCE OF VENUSIAN MESOSPHERE ] yields rd "' 100 days. Thus advective transport is as important as eddy diffusion for tracer transport. In this paper the forces acting on the zonal flow above clouds have been estimated from the cloud-tracked zonal winds and the departure of temperature from radiative equilibrium at the cloud top level by applying the downward control principle. The EP flux associated with a Rossby wave is within the same order of magnitude as the req fired forces; thus the meridional circulation will be driven principally by a Rossby wave. The EP flux associated with gravity waves highly depends on some unkno vn parameters such as the horizontal wave- length; thus the contribution of gravity waves is uncertain. The contribution of horizontal momentum transport by barotropic eddies, which might be important for the maintenance of the superrotation, has not been evaluated in this paper and cannot be dismissed. The results suggest that the concept of a "wave- driven extratropical pump" [e.g., Holton et al., 1995] is valid in the Venusian mesosphere as well as in the terrestrial str tosphere (see Figure 3), although the Venusjan mesosphere is in approximate cyclostrophic balance rather than in geostrophic balance. In the terrestrial stratosphere Rossby or gravity waves, which are presumably generated in the troposphere, induce zonal forces on the mean flow. The forces drive a globalscale extratropical fluid-dynamical suction pump which withdraws air upward and poleward from the tropical troposphere and pushes it poleward and downward into the extratropical troposphere. Acknowledgments. The author is grateful to Y. Matsuds, T. Ogawa, N. Iwagami, and M.D. Yamanaka for helpful discussions and critical comments. The author wishes to thank the anonymous reviewers for constructive suggestions. 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