The use of modern turbulence theory for calculating eddy diffusivities
Modern turbulence theory and applications to obtain analytical solutions to turbulent transport problems
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Modern turbulence theory and applications to obtain analytical solutions to turbulent transport problems
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A Terrier Orion rocket was launched at 0750 Z on 02/25/98 about seven minutes after the Clemson University chemical release rocket. Measurements made of the electron density by a dc probe calibrated by a capacitance probe showed several layers of electron density on a rocket ascent in the altitude range from 90 to 110 km. Rocket descent results showed several but not all of the ascent structure. From power spectral analysis of the measured electron densities, turbulent parameters are derived Measurements were made on rocket ascent and descent by an infrared radiometer of the OH Meinel (3-1) band and O2 singlet delta emissions. Profiles of the emissions are presented and discussed on both rocket ascent and descent an enhancement of the OH emission monitored by the OH radiometer was observed above 90 km. The glow was not defected by the O2 radiometer and was significantly reduced on rocket descent. Using these data and a mechanistic analysis, a profile proportional to atomic oxygen is obtained. This profile is compared to one from the ATOX probe on the rocket. A one-dimensional (1-D) photochemical model that solves the time-dependent continuity equations is used with the rocket data to investigate the odd-oxygen concentration in the near equatorial mesosphere.
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A theory explaining the high aspect ratios for cloud level convection in the Venusian atmosphere is presented. The apparent flatness of large-scale convection cells in the Venusian clouds is accounted for by anisotropic eddy diffusion and radiative transfer effects. Horizontal eddy diffusivities must be at least ten-fold greater than vertical diffusivities. Anisotropy ratios greater than or approximately equal to 1,000 are sufficient to explain the flattening in cases where the vertical eddy diffusivity is greater than or approximately equal to 100,000 sq cm/s and the effects of radiative transfer are negligible. For vertical diffusivity greater than or approximately equal to 100,000 sq cm/s, radiative transfer contributes to the flattening. Radiative transfer alone can not account for the apparent aspect ratios, as this would require vertical heat diffusivities large enough to give a nonphysically high value of convective heat transport.
To investigate the details of hydrocarbon photochemistry on Saturn, we have developed a one-dimensional diurnally averaged model that couples hydrocarbon and oxygen photochemistry, molecular and eddy diffusion, radiative transfer, and condensation. The model results are compared with observations from the Infrared Space Observatory (ISO) to place tighter constraints on molecular abundances, to better define Saturn's eddy diffusion coefficient profile, and to identify important chemical schemes that control the abundances of the observable hydrocarbons in Saturn's upper atmosphere. From the ISO observations, we determine that the column 12 densities of CH3, CH3C2H, and C4H2 above 10 mbar are 4 (sup +2) (sub -1.5) x 10 (exp 13) cm (sup -2), (1.1 plus or minus 0.3) x 10 (exp 15) cm (exp -2), and (1.2 plus or minus 0.3) x 10 (exp 14) cm (sup -2), respectively. The observed ISO emission features also indicate C2H2 mixing ratios of 1.2 (sup +0.9) (sub -0.6) x 10 (exp -6) at 0.3 mbar and (2.7 plus or minus 0.8) x 10 (exp -7) at 1.4 mbar, and a C2H6 mixing ratio of (9 plus or minus 2.5) x 10 (exp -6) at 0.5 mbar. Upper limits are provided for C2H4, CH2CCH2, C3H8, and C6H2 sensitivity of the model results to variations in the eddy diffusion coefficient profile, the solar flux, the CH4 photolysis branching ratios, the atomic hydrogen influx, and key reaction rates are discussed in detail. We find that C4H2 and CH3C2H are particularly good tracers of important chemical processes and physical conditions in Saturn's upper atmosphere, and C2H6 is a good tracer of the eddy diffusion coefficient in Saturn's lower stratosphere. The eddy diffusion coefficient must be smaller than approximately 3 x 10 (exp 4) sq cm s (sup -1) at pressures greater than 1 mbar in order to reproduce the C2H6 abundance inferred from ISO observations. The eddy diffusion coefficients in the upper stratosphere could be constrained by observations of CH3 radicals if the low-temperature chemistry of CH3 were better understood. We also discuss the implications of our modeling for aerosol formation in Saturn's lower stratosphere-diacetylene, butane, and water condense between approximately 1 and 300 mbar in our model and will dominate stratospheric haze formation at nonauroral latitudes. Our photochemical models will be useful for planning observational sequences and for analyzing data from the upcoming Cassini mission.
Vertically stratified tracers such as methane and nitrous oxide tend to have constant mixing ratio surfaces that slope downward toward the poles in the meridional plane. The equilibrium tracer slope results from the competition between the slope steepening effects of advection by the diabatic circulation and the slope flattening effects of quasi-isentropic eddy transport and photochemical loss. The diabatic circulation iself is, however, driven primarily by eddy transports, which maintain the departure of stratospheric temperatures from radiative equilibrium. If the eddy transports are weak, the diabatic circulation is also weak and the slope is small. Using a simple beta-plane channel model and an eddy diffusion parameterization for the eddy potential vorticity and tracer transports, it is shown that the slope is a maximum for a value of eddy diffusion such that the dynamical time scale lies between the radiative and chemical time scales.
Lindzen's (1967) parameterization for the drag and eddy diffusion produced by breaking internal gravity waves in the mesosphere and lower thermosphere is applied to a modified version of the beta-plane channel model of Holton (1982) in which an isotropic source spectrum of waves is specified similar to that given in 1982 by Matsuno (1982). The transmission for each wave component is influenced by Newtonian cooling and by eddy diffusion induced by the breaking of other wave components. In general the waves with smallest Doppler-shifted phase speeds break first and produce sufficient eddy diffusion to significantly raise the breaking heights for the higher speed components. Thus, the wave drag and diffusion is spread through a deep layer and the resulting mean wind profiles for both summer and winter solstice conditions are more realistic than those computed previously by Holton.
A physical model for the effective thermal conductivity of water frost is proposed for application to the full range of frost density. The proposed model builds on the Zehner-Schlunder one-dimensional formulation for porous media appropriate for solid-to-fluid thermal conductivity ratios less than about 1000. By superposing the effects of mass diffusion and eddy convection on stagnant conduction in the fluid, the total effective thermal conductivity of frost is shown to be satisfactorily described. It is shown that the effects of vapor diffusion and eddy convection on the frost conductivity are of the same order. The results also point out that idealization of the frost structure by cylindrical inclusions offers a better representation of the effective conductivity of frost as compared to spherical inclusions. Satisfactory agreement between the theory and the measurements for the effective thermal conductivity of frost is demonstrated for a wide range of frost density and frost temperature.
The altitude distribution of the nitric oxide nightglow was measured with an ultraviolet spectrometer on board Pioneer Venus, in order to study the effects of the distribution on the Venus nightside lower thermosphere transport properties. Limb profiles were obtained with an 8 ms integration period on several orbits near periapsis. The observations were made between P minus 2 min and P plus 4 min, where altitude ranges between 150 and 350 km, and latitude varies from 24 degrees N to 9 degrees S. A method independent of the spacecraft attitude data was used to fit the observed limb profiles, and to find the altitude of the maximum of the layer (115 plus or minus 2 km), and the topside scale height (about 3 km). It is shown that downward transport by diffusion alone is not sufficient, and if vertical motion is parameterized by eddy diffusion, an eddy diffusion coefficient is deduced from the altitude of the layer.
A model has been proposed for the momentum eddy diffusivity induced by free stream turbulence intensity and integral length scale. The eddy diffusivity model is applied to a cylinder situated in a uniform crossflow in the presence of free stream turbulence. Numerical solution of the governing momentum and energy equations with the proposed eddy diffusivity model yielded results for the skin friction coefficient and the Nusselt number. The numerical predictions of the present work are compared with experimental data and the agreement between the two is seen to be very good.
A model has been proposed for the momentum eddy diffusivity induced by free stream turbulence intensity and integral length scale. The eddy diffusivity model is applied to the stagnation point of a cylinder situated in a uniform crossflow in the presence of free stream turbulence. A numerical solution of the governing momentum and energy equations with the proposed eddy diffusivity model yielded results for the skin friction coefficient and the Nusselt number. The numerical predictions of the present work are compared with experimental data and the agreement between the two is seen to be very good.
The 'standard' accretion-disk model of the solar nebula is examined together with its basic equations, which are solved for the steady-state case. It is shown that, for this model of the solar nebula, the efficiency of mixing the products of thermochemical processing from small to large disk radii depends not on the magnitude of the eddy diffusivity but only on the ratio k between the eddy diffusivity and the eddy viscosity. In most cases, this ratio k is probably of order of unity or less, implying that most of the solar nebula was not contaminated by the consequences of thermochemical equilibria that were established at 'small' disk radii. It is noted that, while this condition is almost certainly satisfied if the physical process responsible for viscosity is thermal convection or waves, it has uncertain validity during the early phases of disk evolution where accretion-induced shear instabilities may dominate.