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NASA NTRS1992

Hydrocarbons and eddy mixing in Neptune's atmosphere

The most recent analysis of the Voyager ultraviolet solar occultation observations at Neptune indicates a methane mixing ratio 1-10 times above saturation in the lower stratosphere, unlike the value of 500-1000 times saturation which was suggested just before the encounter of Voyager with Neptune. The acetylene mixing ratio in the 0.1 mb region is found to be (6-8) x 10 exp -8, which is approximately a factor of 3 lower than the value reported in our Voyager/Science paper. The eddy diffusion coefficient at the homopause (1-3) x 10 exp 7 sq cm/s, is found to be more like that of Saturn than Uranus. The new results on CH4, C2H2 and K have strong implications for the stratospheric temperatures, now warmer, and the source of heating. Furthermore, the pre-Voyager models of the hydrocarbon hazes need to be revised in view of the new model atmosphere.

Atreya, S. K.↗
NASA NTRS1993

A solar dynamo surface wave at the interface between convection and nonuniform rotation

A simple dynamo surface wave is presented to illustrate the basic principles of a dynamo operating in the thin layer of shear and suppressed eddy diffusion beneath the cyclonic convection in the convection zone of the sun. It is shown that the restriction of the shear delta(Omega)/delta(r) to a region below the convective zone provides the basic mode with a greatly reduced turbulent diffusion coefficient in the region of strong azimuthal field. The dynamo takes on the character of a surface wave tied to the lower surface z = 0 of the convective zone. There is a substantial body of evidence suggesting a fibril state for the principal flux bundles beneath the surface of the sun, with fundamental implications for the solar dynamo.

Parker, E. N.↗
NASA NTRS1993

The distribution of hydrocarbons in Neptune's upper atmosphere

The distribution of hydrocarbons in the upper atmosphere of Neptune is determined on the basis of data from the Voyager UVS solar occultation experiment. Densities are inferred from the transmission properties of the atmosphere measured by the UVS. The CH4 mole fraction in the lower stratosphere is between 0.0006 and 0.005. It is inferred that CH4 in Neptune's lower stratosphere is oversaturated by at least a factor of 10, and possibly by as much as a factor of 100. The density of C2H6 reaches values of 3 x 10 exp 9/cu cm near 100 microbar; a C2H6 production efficiency of 35 +15/-5 percent is derived. The eddy diffusion coefficient is approximately constant at a value of 10,000 sq cm/s at altitudes below 300 km and increases at higher altitudes as the pressure to the 0.75 power. A mole fraction of 0.001 is found to be consistent with the CH4 vapor pressure at 3.4 mbar; consequently, CH4 ice particles must reach this level to produce the inferred oversaturation.

Yelle, Roger V.↗
NASA NTRS1955

Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers

The expression for eddy diffusivity from a previous analysis was modified in order to account for the effect of kinematic viscosity on the turbulence in the region close to a wall. By using the modified expression, good agreement was obtained between predicted and experimental results for heat and mass transfer at Prandtl and Schmidt numbers between 0.5 and 3000. The effects of length-to-diameter ratio and of variable viscosity were also investigated for a wide range of Prandtl numbers.

Deissler, Robert G↗
NASA NTRS1993

Eddy mixing coefficient upper limit derived from the photochemical balance of O2

This work is based on the study of the photochemical balance of molecular oxygen in the martian atmosphere by using a one-dimensional model of photochemical reactions involving species derived from CO2 and H2O. The model is basically similar to one used previously for the study of the regulation of CO on a global scale, but the chemical rates are taken from another source. In the present scheme, the regulation of molecular oxygen is studied over timescales of the order of its photochemical lifetime (approximately equals 30 yr), which is much shorter than typical escape timescales. Thus, the escape fluxes are fixed to the values given by 3 and 4. We examine the calculated equilibrium abundances of O2 for given thermal, eddy diffusion coefficients and H2O profiles. The thermal profile is taken from in the lower atmosphere. At higher levels, in order to include the diurnal and seasonal thermal profile variability, we have also used the IRTM data. In order to study the influence of both temperature and pressure profiles on the O2 mixing ratio, we have made several tests corresponding to different martian seasons. The results show that the influence of pressure and temperature is quantitatively weak compared to the one of K and of the water vapor density (H2O). Thus, in the following we have fixed the pressure at the surface to a value of 7 mbar and we have used unique standard thermal profile corresponding to a profile roughly averaged over the year, the season, and the day: T equal 205 K at 0 km altitude, 175 K at 25 km, and 145 K at 50 km.

Rosenqvist, J.↗
NASA NTRS1994

Sources and distribution of NO(x) in the upper troposphere at northern midlatitudes

A simple quasi 2-D model is used to study the zonal distribution of NO(x). The model includes vertical transport in form of eddy diffusion and deep convection, zonal transport by a vertically uniform wind, and a simplified chemistry of NO, NO2 and HNO3. The NO(x) sources considered are surface emissions (mostly from the combustion of fossil fuel), lightning, aircraft emissions, and downward transport from the stratosphere. The model is applied to the latitude band of 40 deg N to 50 deg N during the month of June; the contributions to the zonal NO(x) distribution from the individual sources and transport processes are investigated. The model predicted NO(x) concentration in the upper troposphere is dominated by air lofted from the polluted planetary boundary layer over the large industrial areas of Eastern North America and Europe. Aircraft emissions are also important and contribute on average 30 percent. Stratospheric input is minor about 10 percent, less even than that by lightning. The model provides a clear indication of intercontinental transport of NO(x) and HNO3 in the upper troposphere. Comparison of the modelled NO profiles over the Western Atlantic with those measured during STRATOZ 3 in 1984 shows good agreement at all altitudes.

Rohrer, Franz↗
NASA NTRS1994

Venus O2 visible and IR nightglow: Implications for lower thermosphere dynamics and chemistry

The National Center for Atmospheric Research thermospheric general circulation model for the Venus thermosphere is modified to examine two observed night airglow features, both of which serve as sensitive tracers of the thermospheric circulation. New O2 nightglow data from the Pioneer Venus Orbiter (PVO) star tracker (O2 Herzberg II at 400-800 nm) and ground-based telescopes (O2 IR at 1.27 microns) yield additional model constraints for estimating Venus winds over 100-130 km. Atomic oxygen, produced by dayside CO2 photolysis peaking near 110 km, and transported to the nightside by the global wind system, is partially destroyed through three-body recombination, yielding the O2 Herzberg II visible nightglow. This emission is very sensitive to horizontal winds at altitudes between 100 and 130 km. Other trace species catalytic reactions also contribute to the production of the very strong nightside infrared (1.27 microns) emission. This paper examines the dynamical and chemical implications of these new data using the Venus thermospheric general circulation model (VTGCM) as an analysis tool. Three-dimensional calculations are presented for both solar maximum and solar medium conditions, corresponding to early PVO (1979-1981) and PVO entry (mid-1992) time periods. Very distinct periods are identified in which zonal winds are alternately weak and strong in the Venus lower thermosphere. VTGCM sensitivity studies are conducted to assess the impacts of potential changes in thermospheric zonal and day-to-night winds, and eddy diffusion on the corresponding nightglow intensities. It appears that cyclostrophic balance extends above 80 km periodically, owing to a reversal of the upper mesosphere latitudinal temperature gradient, and thereby producing strong zonal winds and correspondingly modified O2 nightglow distributions that are observed.

Bougher, S. W.↗
NASA NTRS1994

CO2 cooling in terrestrial planet thermospheres

We examine the recent progress in the debate on the CO2-O relaxation rate, its temperature dependence, and its corresponding impact on the thermospheric heat budgets of Venus, Earth, and Mars. This comparative approach provides the broadest range of conditions under which a common CO2-O relaxation rate should provide consistent results. New global mean calculations are presented for the heat budgets of these three planets using large CO2-O relaxation rates that have been inferred recently from Earth CO2 radiance measurements and laboratory studies. Results indicate that available Venus and Mars data constrain the CO2-O relaxation rate to be 2-4 x 10(exp -12)/cu cm/s at 300 K. For Venus, this strong cooling serves as an effective thermostat that gives rise to a small variation of thermospheric temperatures over the solar cycle, just as observed. Conversely, CO2 cooling does not appear to be dominant in the dayside heat budget of the Mars thermosphere over most of the solar cycle. For the Earth, this strong cooling implies that the lower thermosphere does not typically require significant eddy diffusion or heat conduction. However, global-scale dynamics or an additional heating mechanism may be needed to restore calculated temperatures to observed values when relaxation rates exceeding 2 x 10(exp -12)/cu cm/s are employed.

Bougher, S. W.↗
NASA NTRS1995

Photochemical modeling of Titan's atmosphere

We have developed a new photochemical model of Titan's atmosphere which includes all the important compounds and reactions in spherical geometry from the surface to 1240 km. Compared to the previous model of Yung et al. (1984), the most significant recent change in the reactions used is the updated methane dissociation scheme (Mordaunt et al. 1993). Moreover, the transfer of the solar radiation in the atmosphere and the photolysis rates have been calculated by using a Monte Carlo code. Finally, the eddy diffusion coefficient profile is adjusted in order to fit the mean vertical distribution of HCN retrieved from millimeter groundbased observations of Tanguy et al. (1990); using new values for the boundary flux of atomic nitrogen (Strobel et al. 1992). We have run the model in both steady-state and diurnal modes, with 62 species involved in 249 reactions. There is little difference between diurnal and steady-state results. Overall our results are in a closer agreement with the abundances inferred from the Voyager infrared measurements at the equator than the Yung et al. results. We find that the catalytic scheme for H recombination invoked by Yung et al. only slightly improves the model results and we conclude that this scheme is not essential to fit observations.

Toublanc, D.↗
NASA NTRS1996

A Computational Fluid Dynamic and Heat Transfer Model for Gaseous Core and Gas Cooled Space Power and Propulsion Reactors

A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor.

Anghaie, S.↗
NASA NTRS1996

Transport Coefficients in weakly compressible turbulence

A theory of transport coefficients in weakly compressible turbulence is derived by applying Yoshizawa's two-scale direct interaction approximation to the compressible equations of motion linearized about a state of incompressible turbulence. The result is a generalization of the eddy viscosity representation of incompressible turbulence. In addition to the usual incompressible eddy viscosity, the calculation generates eddy diffusivities for entropy and pressure, and an effective bulk viscosity acting on the mean flow. The compressible fluctuations also generate an effective turbulent mean pressure and corrections to the speed of sound. Finally, a prediction unique to Yoshizawa's two-scale approximation is that terms containing gradients of incompressible turbulence quantities also appear in the mean flow equations. The form these terms take is described.

Rubinstein, Robert↗
NASA NTRS1995

An Analysis of Neptune's Stratospheric Haze Using High-Phase-Angle Voyager Images

We have inverted high-phase-angle Voyager images of Neptune to determine the atmospheric extinction coefficient as a function of altitude and the scattering phase function at a reference altitude. Comparisons between theoretical model and observations help separate the contributions from molecular Rayleigh and aerosol scattering and help determine the variation of the aerosol size, concentration, and scattering properties with altitude. Further comparisons between models and data allow us to place constraints on the location and composition of the hazes, the concentration and downward flux of certain condensible hydrocarbon gases, the eddy diffusion coefficient in the lower stratosphere, and the thermal profile in parts of Neptune's stratosphere. We find that a distinct stratospheric haze layer exists near 12(sub -1, sup +1) mbar in Neptune's lower stratosphere, most probably due to condensed ethane. The derived stratospheric haze production rate of 1.0(sub -0.3, sup +0.2) x 10(exp -15) g cm(exp -2) sec(exp -1) is substantially lower than photochemical model predictions. Evidence for hazes at higher altitudes also exists. Unlike the situation on Uranus, large particles (0.08-0.11 microns) may be present at high altitudes on Neptune (e.g., near 0.5 mbar), well above the region in which we expect the major hydrocarbon species to condense. Near 28 mbar, the mean particle size is about 0.13(sub -0.02, sup +0.02) microns with a concentration of 5(sub -3, sup +3) particles cm(exp -3). The cumulative haze extinction optical depth above 15 mbar in the clear filter is approx. 3 x 10(exp -3), and much of this extinction is due to scattering rather than absorption; thus, if our limb-scan sites are typical, the hazes cannot account for the stratospheric temperature inversion on Neptune and may not contribute significantly to atmospheric heating. We compare the imaging results with the results from other observations, including those of the Voyager Photopolarimeter Subsystem, and discuss differences between Neptune and Uranus.

Moses, Julianne I.↗
NASA NTRS1997

Numerical Study of Stratified Charge Combustion in Wave Rotors

A wave rotor may be used as a pressure-gain combustor effecting non-steady flow, and intermittent, confined combustion to enhance gas turbine engine performance. It will be more compact and probably lighter than an equivalent pressure-exchange wave rotor, yet will have similar thermodynamic and mechanical characteristics. Because the allowable turbine blade temperature limits overall fuel/air ratio to sub-flammable values, premixed stratification techniques are necessary to burn hydrocarbon fuels in small engines with compressor discharge temperature well below autoignition conditions. One-dimensional, unsteady numerical simulations of stratified-charge combustion are performed using an eddy-diffusivity turbulence model and a simple reaction model incorporating a flammability limit temperature. For good combustion efficiency, a stratification strategy is developed which concentrates fuel at the leading and trailing edges of the inlet port. Rotor and exhaust temperature profiles and performance predictions are presented at three representative operating conditions of the engine: full design load, 40% load, and idle. The results indicate that peak local gas temperatures will result in excessive temperatures within the rotor housing unless additional cooling methods are used. The rotor itself will have acceptable temperatures, but the pattern factor presented to the turbine may be of concern, depending on exhaust duct design and duct-rotor interaction.

Nalim, M. Razi↗
NASA NTRS1995

Photochemistry of Triton's Atmosphere and Ionosphere

The photochemistry of 32 neutral and 21 ion species in Triton's atmosphere is considered. Parent species N2, CH4, and CO (with a mixing ratio of 3 x 10(exp -4) in our basic model) sublime from the ice with rates of 40, 208, and 0.3 g/sq cm/b.y., respectively. Chemistry below 50 km is driven mostly by photolysis of methane by the solar and interstellar medium Lyman-alpha photons, producing hydrocarbons C2H4, C2H6, and C2H2 which form haze particles with precipitation rates of 135, 28, and 1.3 g/sq cm/b.y., respectively. Some processes are discussed which increase the production of HCN (by an order of magnitude to a value of 29 g/sq cm/b.y.) and involve indirect photolysis of N2 by neutrals. Reanalysis of the measured methane profiles gives an eddy diffusion coefficient K = 4 x 10(exp 3)sq cm/s above the tropopause and a more accurate methane number density near the surface, (3.1 +/- 0.8)x IO(exp 11)/cu cm. Chemistry above 200 km is driven by the solar EUV radiation (lambda less than 1000 A) and by precipitation of magnetospheric electrons with a total energy input of 10(exp 8) W (based on thermal balance calculations). The most abundant photochemical species are N, H2, H, 0, and C. They escape with the total rates of 7.7 x 10(exp 24)/ s, 4.5 x 10(exp 25)/s, 2.4 x 10(exp 25)/s, 4.4 x 10(exp 22)/s, and 1.1 x 10(exp 24), respectively. Atomic species are transported to a region of 50-200 km and drive the chemistry there. Ionospheric chemistry explains the formation of an E region at 150-240 km with HCO(+) as a major ion, and of an F region above 240 km with a peak at 320 km and C(+) as a major ion. The ionosphere above 500 km consists of almost equal densities of C(+) and N(+) ions. The model profiles agree with the measured atomic nitrogen and electron density profiles. A number of other models with varying rate coefficients of some reactions, differing properties of the haze particles (chemically passive or active), etc., were developed. These models show that there are four basic unknown values which have strong impacts on the composition and structure of the atmosphere and ionosphere. These values and their plausible ranges are the CO mixing ratio f(sub co) = 10(exp -4) - 10(exp -3), the magnetospheric electron energy input (1 +/- 0.5) x 10(exp 8) W, the rate coefficient of charge-exchange reaction N2(+) + C(kappa) = 10(exp -11) - 10(exp -10)cu cm/s, and the ion escape velocity upsilon(sub i) approx. equals 150 cm/s.

Krasnopolsky, Vladimir A.↗
NASA NTRS1995

Photochemistry of Triton's Atmosphere and Ionosphere

The photochemistry of 32 neutral and 21 ion species in Triton's atmosphere is considered. Parent species N2, CH4, and CO (with a mixing ratio of 3 x 10(exp -4) in our basic model) sublime from the ice with rates of 40, 208, and 0.3 g/sq cm/b.y., respectively. Chemistry below 50 km is driven mostly by photolysis of methane by the solar and interstellar medium Lyman-alpha photons, producing hydrocarbons C2H4, C2H6, and C2H2 which form haze particles with precipitation rates of 135, 28, and 1.3 g/sq cm/b.y., respectively. Some processes are discussed which increase the production of HCN (by an order of magnitude to a value of 29 g/sq cm/b.y.) and involve indirect photolysis of N2 by neutrals. Reanalysis of the measured methane profiles gives an eddy diffusion coefficient K = 4 x 10(exp 3) sq cm/s above the tropopause and a more accurate methane number density near the surface, (3.1 +/- 0.8) x 10(exp 11)/cc cm. Chemistry above 200 km is driven by the solar EUV radiation (lambda less than 1000 A)) and by precipitation of magnetospheric electrons with a total energy input of 10(exp 8) W (based on thermal balance calculations). The most abundant photochemical species are N, H2, H, O, and C. They escape with the total rates of 7.7 x 10(exp 24)/ s, 4.5 x 10(exp 25)/ s, 2.4 x 10(exp 25)/ s, 4.4 x 10(exp 22)/ s, and 1.1 x 10(exp 24)/ s, respectively. Atomic species are transported to a region of 50-200 km and drive the chemistry there. Iono- spheric chemistry explains the formation of an E region at 150-240 km with HCO(+) as a major ion, and of an F region above 240 km with a peak at 320 km and C(+) as a major ion. The ionosphere above 500 km consists of almost equal densities of C(+) and N(+) ions. The model profiles agree with the measured atomic nitrogen and electron density profiles. A number of other models with varying rate coefficients of some reactions, differing properties of the haze particles (chemically passive or active), etc., were developed. These models show that there are four basic unknown values which have strong impacts on the composition and structure of the atmosphere and ionosphere. These values and their plausible ranges are the CO mixing ratio f(sub co) = 10(exp -4)- 10(exp -3), the magnetospheric electron energy input (1 +/- 0.5) x 10(exp 8) W, the rate coefficient of charge-exchange reaction N2(+) + Ck = 10(exp -11)-10(exp -10)cc cm/s, and the ion escape velocity upselon(sub i) approx. 150 cm/s.

Krasnopolsky, Vladimir A.↗
NASA NTRS1998

Transport Between the Tropical and Midlatitude Lower Stratosphere: Implications for Ozone Response to High Speed Civil Transport Emissions

Several recent studies have quantified the air exchange rate between the tropics and midlatitudes in the lower stratosphere using airborne and satellite measurements of chemical species. It is found that the midlatitude air is mixed into the tropical lower stratosphere with a replacement timescale of 13.5 months (with 20% uncertainty) for the region from the tropopause to 21 km and at least 18 months for the region of 20-28 km. These estimates are used to adjust the horizontal eddy diffusion coefficients, K(sub yy), in a two-dimensional chemistry transport model. The value of K(sub yy) previously used to simulate the subtropical barrier, 0.03 x 10(exp 6)sq m/s, generates an exchange time of about 4 years, and the model without subtropical barrier (K(sub yy) = 0.3 x 10(exp 6)sq m/s) has an exchange time of 5 months. Adjusting the K(sub yy) to 0.13 x 10(exp 6) sq m/s from the tropopause to 21 km and 0.07 x 10(exp 6)sq m/s above 21 km produces the exchange timescales which match the estimates deduced from the measurements. The subtropical barrier prevents the engine emissions of the high-speed civil transport (HSCT) aircraft from being transported into the tropics and subsequently lifted into the upper atmosphere or mixed into the southern hemisphere. The model results show that the calculated ozone response to HSCT aircraft emissions using the K(sub yy), adjusted to observed mixing rates is substantially smaller than that simulated without the subtropical barrier.

Shia, R.-L.↗
NASA NTRS1999

The Role of Gravity Waves in Generating Equatorial Oscillations in Modulating Atmospheric Tides

We discuss a Numerical Spectral Mode (NSM) that extends from the ground up into the thermosphere and incorporates Hines' Doppler spread parameterization (DSP) for small scale gravity waves (GW). This model is applied to describe the seasonal variations in the mean zonal circulation, the semi-annual and quasi-biennial oscillations (SAO and QBO), as well as the tides and planetary waves in the middle atmosphere. Initial results showed that this model can reproduce the salient features observed, including the QBO extending into the upper mesosphere inferred from UARS measurements. The model has now been extended to simulate also: (a) the zonal circulation of the lower stratosphere and upper troposphere, and (b) the upwelling at equatorial latitudes associated with the Brewer Dobsen circulation that affects the dynamics significantly as pointed out by Dunkerton. Upward vertical winds increase the period of the QBO observed from the ground. To compensate for that, one needs to increase in the model the eddy diffusivity and the GW momentum flux, bringing the latter closer to values recommended in the DSP. This development is conducive to extending the QBO and SAO to higher latitudes through global scale momentum redistribution. Multi-year interannual oscillations are generated through wave filtering by the solar driven annual oscillation in the zonal circulation. In a 3D version of the model, wave momentum is absorbed and dissipated by tides and planetary waves. A somewhat larger GW source (well within the DSP range) is then required to generate realistic QBO and SAO amplitudes. Since GW momentum is deposited in the altitude regime of increasing winds, the amplitude of the diurnal tide is amplified and its vertical wavelength is reduced at altitudes between 70 and 120 km. Wave filtering by the mean zonal circulation causes the GW flux to peak during equinox, and this produces a large semi-annual variation in the tide that has been observed on UARS. Without the diurnal tide, the semidiurnal tide would also be modulated in this way. But the diurnal tide filters out the GW preferentially during equinox, so that the semidiurnal tide tends to peak during solstice. Under the influence of GW, the tides are modulated significantly by planetary waves that are generated preferentially during solstice in part due to baroclinic instability.

Mayr, H. G.↗
NASA NTRS1999

Properties of QBO and SAO Generated by Gravity Waves

We present an extension for the 2D (zonal mean) version of our Numerical Spectral Mode (NSM) that incorporates Hines' Doppler spread parameterization (DSP) for small scale gravity waves (GW). This model is applied to describe the seasonal variations and the semi-annual and quasi-biennial oscillations (SAO and QBO). Our earlier model reproduced the salient features of the mean zonal circulation in the middle atmosphere, including the QBO extension into the upper mesosphere inferred from UARS measurements. In the present model we incorporate also tropospheric heating to reproduce the upwelling at equatorial latitudes associated with the Brewer-Dobson circulation that affects significantly the dynamics of the stratosphere as Dunkerton had pointed out. Upward vertical winds increase the period of the QBO observed from the ground. To compensate for that, one needs to increase the eddy diffusivity and the GW momentum flux, bringing the latter closer to values recommended in the DSP. The QBO period in the model is 30 months (mo), which is conducive to synchronize this oscillation with the seasonal cycle of solar forcing. Multi-year interannual oscillations are generated through wave filtering by the solar driven annual oscillation in the zonal circulation. Quadratic non-linearities generate interseasonal variations to produce a complicated pattern of variability associated with the QBO. The computed temperature amplitudes for the SAO and QBO are in substantial agreement with observations at equatorial and extratropical latitudes. At high latitudes, however, the observed QBO amplitudes are significantly larger, which may be a signature of propagating planetary waves not included in the present model. The assumption of hydrostatic equilibrium not being imposed, we find that the effects from the vertical Coriolis force associated with the equatorial oscillations are large for the vertical winds and significant for the temperature variations even outside the tropics but are relatively small for the zonal winds.

Mayr, H. G.↗