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A NEW MODEL FOR MIXING BY DOUBLE-DIFFUSIVE CONVECTION (SEMI-CONVECTION). III. THERMAL AND COMPOSITIONAL TRANSPORT THROUGH NON-LAYERED ODDC

Oscillatory double-diffusive convection (ODDC; also known as semi-convection) refers to a type of double-diffusive instability that occurs in regions of planetary and stellar interiors that have a destabilizing thermal stratification and a stabilizing mean molecular weight stratification. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and chemical species by ODDC. Rosenblum et al. first showed that ODDC can either spontaneously form layers that significantly enhance the transport of heat and chemical species compared to microscopic transport or remain in a state dominated by large-scale gravity waves, in which there is a more modest enhancement of the turbulent transport rates. Subsequent studies in this series focused on identifying under what conditions layers form and quantifying transport through layered systems. Here we proceed to characterize transport through systems that are unstable to ODDC, but do not undergo spontaneous layer formation. We measure the thermal and compositional fluxes in non-layered ODDC from both two-dimensional (2D) and 3D numerical simulations, and show that 3D simulations are well approximated by similar simulations in a 2D domain. We find that the turbulent mixing rate in this regime is weak and can, to a first-level approximation, be neglected. We conclude by summarizing the findings of papers I through III into a single prescription for transport systems unstable to ODDC.

79 ASTRONOMY AND ASTROPHYSICS↗

Theoretical study of reactive and nonreactive turbulent coaxial jets

The hydrodynamic properties and the reaction kinetics of axisymmetric coaxial turbulent jets having steady mean quantities are investigated. From the analysis, limited to free turbulent boundary layer mixing of such jets, it is found that the two-equation model of turbulence is adequate for most nonreactive flows. For the reactive flows, where an allowance must be made for second order correlations of concentration fluctuations in the finite rate chemistry for initially inhomogeneous mixture, an equation similar to the concentration fluctuation equation of a related model is suggested. For diffusion limited reactions, the eddy breakup model based on concentration fluctuations is found satisfactory and simple to use. The theoretical results obtained from these various models are compared with some of the available experimental data.

Gupta, R. N.↗

Can stochastic, dissipative wave fields be treated as random walk generators

A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.

Weinstock, J.↗

Implications of three-dimensional tracer studies for two-dimensional assessments of the impact of supersonic aircraft on stratospheric ozone

A 2D model which uses residual circulation and diffusion and a 3D model which uses winds from a stratospheric data assimilation system are used to estimate transport and dispersion of supersonic aircraft exhaust in the lower stratosphere. The seasonal behavior of the exhaust fields in the two models are is similar, but there is a significant difference in the placement of stratosphere/troposphere exchange in the two models. In the 2D model, exhaust transport to the troposphere occurs mostly at high latitudes, while in the 3D model it occurs at middle latitudes and is clearly associated with synoptic scale events. This may be particularly important to assessment calculations, as the pollutant source is mostly in middle latitudes. The 3D model is also used to examine the transport and dispersion of exhaust in three typical flight corridors: North Atlantic, North Pacific, and tropical. There are no systematic differences that suggest that one corridor is inherently more or less polluting than another.

Douglass, Anne R.↗

Magnetic field amplification in nonlinear diffusive shock acceleration including resonant and non-resonant cosmic-ray driven instabilities

We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-Alfvénic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (∼eV) injected at the viscous subshock to the escape of the highest energy CRs (∼PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification, and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the downstream proton temperature, the magnetic fluctuation spectra, and accelerated particle spectra. A parameter survey is included where we vary shock parameters, the mode of magnetic turbulence generation, and turbulence cascading. From our survey results, we obtain scaling relations for the maximum particle momentum and amplified magnetic field as functions of shock speed, ambient density, and shock size.

79 ASTRONOMY AND ASTROPHYSICS↗

Characterization of Grain‐Size Distribution, Thermal Conductivity, and Gas Diffusivity in Variably Saturated Binary Sand Mixtures

Core Ideas Parameterized models are relevant to applications where different porous media mixtures are used. Models include a grain‐size distribution function to describe bimodal behavior for binary mixtures. Improved model describes observed thermal conductivity–saturation relations for binary mixtures. Combined Buckingham–Penman model used to describe observed gas diffusivity–air content relations. This work is relevant for proper simulation of mixed porous media. Characterization of differently textured porous materials, as well as different volumetric porous media mixtures, in relation to mass and heat transport is vital for many engineering and research applications. Functional relations describing physical (e.g., grain‐size distribution, total porosity), thermal, and gas diffusion properties of porous media and mixtures are necessary to optimize the design of porous systems that involve heat and gas transport processes. However, only a limited number of studies provide characterization of soil physical, thermal, and gas diffusion properties and the functional relationships of these properties under varying soil water contents, especially for soil mixtures, complicating optimization efforts. To better understand how mixing controls the physical, thermal, and gas diffusion properties of porous media, a set of laboratory experiments was performed using five volumetric mixtures of coarse‐ and fine‐grained sand particles. For each mixture, the grain‐size distribution (GSD), thermal conductivity, and gas diffusivity were obtained and parameterized using existing and suggested parametric models. Results show that the extended, two‐region Rosin–Rammler particle‐size distribution model proposed in this study could successfully describe the bimodal behavior of the GSD of binary mixtures. Further, the modified Côté and Konrad thermal conductivity model adequately described the thermal conductivity–water saturation relations observed in different mixtures. The proposed simple soil‐gas diffusivity descriptive model parameterized the upper limit, average, and lower limit behavior in gas diffusivity–air content relations in apparently texture‐invariant gas diffusivity data. Results further show a close analogy between gas diffusivity and thermal conductivity and their variation with saturation across different binary mixtures. Overall, the results of the study provide useful numerical insight into the physical, thermal, and gas transport characteristics of binary mixtures, with wide implications for future engineering and research applications that involve multicomponent porous systems.

Deepagoda, T. K. K. Chamindu↗

A BABCOCK–LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES

Babcock–Leighton type-solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock–Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that the presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in the butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of the butterfly wing to an antisolar type. A butterfly diagram constructed from the middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow speed is strong enough, of similar order of magnitude as the surface flow speed.

79 ASTRONOMY AND ASTROPHYSICS↗

Study on impact of Cr and Mo on diffusion of H in 2.25Cr1Mo steel using first-principle calculations

Chrome-molybdenum steel (2.25Cr1Mo steel) is one of the main materials of a steam generator (SG) in high-temperature reactor-pebblebed modules (HTR-PM). It is essential to analyze the source term of tritium in this material, because the behavior of tritium in a SG is important for performing source term analysis in normal and accident conditions. In this article, the diffusion behavior of H atom in 2.25Cr1Mo steel was calculated to estimate the diffusivity of tritium using first-principles density functional theory. To develop and simplify the model of hydrogen diffusion in 2.25Cr1Mo steel, the impact of Cr and Mo on the diffusion of hydrogen in bcc-Fe were first calculated, all the possible diffusion paths were considered, and the minimum energy path was obtained. The diffusion activation energy and pre-exponential factor of the diffusion coefficient were obtained from Vienna Ab initio Simulation Package combined with the climbing image-nudged elastic band method. Here the results indicate that the minimum energy path for the impurity H atom is from one tetrahedral interstitial site to an adjacent tetrahedral interstitial site. The function of the diffusion coefficient of H in 2.25Cr1Mo steel with temperature T can be expressed as D = 1.486 X 10 -7 x ($\frac{-16.350kJ/mol}{RT}$) (M2/s). The diffusion coefficient of our calculation and some of the previous experiments have an excellent quantitative agreement, which indicates the reliability of our crystalline model and the practicability of the present theoretical approach. More importantly, the computational results in this work can be treated as a good screening method to collect reasonable experimental data, which will provide a good reference for tritium source term evaluation in the SG of the HTR-PM.

36 MATERIALS SCIENCE↗