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Convective instability in superposed fluid and anisotropic porous layers

The onset of thermal convection due to heating from below in a system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity is studied. The linear perturbation equations are solved numerically. It is found that the effects of anisotropy on the onset of thermal convection are most profound for small values of the depth ratio xi (ratio of fluid layer thickness to porous layer thickness), since in that case, the onset of convection corresponds to significant motion in both layers. For fixed vlues of the vertical permeability in the porous medium, decreasing the value of zeta (ratio of horizontal to vertical permeability) leads to stabilization of the superposed layer configuration because of increased resistance to motion in the porous medium. For larger values of xi, the onset of motion is increasingly confined to the fluid layer, with the transport of heat through the porous layer occurring primarily by conduction. Accordingly, the influence of zeta on the stability characteristics for larger xi is less significant than the effects of an anisotropic thermal conductivity.

Chen, Falin↗

Convection during Thermally Unstable Solidification of Pb-Sn in a Magnetic Field

Convection and macrosegregation in directionally solidified hypoeutectic Pb-38 wt pct Sn and hypereutectic Pb-64.5 wt pct Sn have been examined during upward and downward growth. Temperature fluctuations are observed along the length of the melt column during downward growth. With increasing Rayleigh number, these fluctuations change from none, to cyclic, to time periodic having multiple harmonics, and finally to random. At the higher convective driving force of 350 K temperature inversion, the transverse magnetic field decreased convective levels, strong random temperature fluctuations (flows) becoming smaller and periodic. The maximum field of 0.45 T was unable to completely eliminate convection. For the lower convective driving force of 150 K temperature inversion, the 0.05 T magnetic field decreased flows, and at 0.15 T, the field caused a dramatic decrease in the characteristic frequency of the temperature fluctuations, indicating a change in the nature of the flow, the waveform of the temperature fluctuations changing from sinusoidal to a pulsed wave. Temperature fluctuations and time delays between thermocouples were used to estimate flow velocities. Irrespective of the convection in the bulk melt (ahead of the mushy zone), longitudinal macrosegregation occurs only if the interdendritic melt mixes with the bulk melt.

Song, H.↗

Effect of magnetospheric convection on thermal plasma in the inner magnetosphere

The effects of E x B convection on the distribution of plasma parameters in the inner magnetosphere have been examined. Analytical solutions describing density distributions along convective trajectories in the equatorial plane have been found. These solutions suggest the following dependence of plasma concentration n on the magnetic field B along convective trajectories: n proportional to B(exp alpha), where the parameter alpha varies between alpha is less than or = between 4/3 and 2. The alpha = 2 case corresponds to disregarding transport parallel to B. The lower bound alpha = 4/3 describes the situation when parallel transport dominates over convective motions perpendicular to B. A solution has also been obtained describing the effect of convection on diffusive equilibrium profiles in the dayside plasmasphere. In addition, ion temperature variations due to adiabatic effects associated with plasma convection have been analyzed in detail. Convective drifts lead to ion temperature anisotropies with the value and sign of the anisotropy contingent on density and temperature variations, local time, and the location of the convective trajectory with respect to the location of the plasmapause. We have also found that convective motions lead to a substantial exchange of energy between the ionosphere and the plasmasphere through electron heat fluxes.

Khazanov, G. V.↗

Studies of heat-source driven natural convection: A numerical investigation

Thermal convection driven by uniform volumetric energy sources was studied in a horizontal fluid layer bounded from above by a rigid, isothermal surface and from below by a rigid, zero heat-flux surface. The side walls of the fluid domain were assumed to be rigid and perfectly insulating. The computations were formally restricted to two-dimensional laminar convection but were carried out for a range of Rayleigh numbers which spans the regimes of laminar and turbulent flow. The results of the computations consists of streamline and isotherm patterns, horizontally averaged temperature distributions, and horizontally averaged Nusselt numbers at the upper surface. Flow and temperature fields do not exhibit a steady state, but horizontally averaged Nusselt numbers reach limiting, quasi-steady values for all Rayleigh numbers considered. Correlations of the Nusselt number in terms of the Rayleigh and Prandtl numbers were determined.

Emara, A. A.↗

Simulation of triglycine sulfate crystal growth in space

Consideration is given to the numerical simulation of the solution growth of triglycine sulfate in space, with heat transfer, mass transfer, buoyancy-driven convection, the dependence of solubility on temperature, and finite interface kinetics taken into account. In the bulk solution, weak thermal convection was established quickly. The thermal convection then becomes dominated by solutionally driven motion. The convection due to the steady background g is predicted to influence both the growth rate and the crystal morphology. The time required for buoyancy-driven convection to influence the growth rate depends on the magnitude of g, i.e., more time for smaller g. Under the same cooling condition, the average growth rate increases as the magnitude of g increases. A steady average growth rate of 1.0 mm/d can be obtained when a properly designed cooling rate is applied to the sting. The most uniform growth is obtained when the g vector is aligned such that the solution flows normal towards the center of the crystal surface.

Sun, Jianhua↗

Effects of thermal-solutal convection on temperature and solutal fields under various gravitational orientations

Semiconductor crystals such as Hg(1-x)CD(x)Te grown by unidirectional solidification Bridgmann method have shown compositional segregations in both the axial and radial directions. Due to the wide separation between the liquidus and the solidus of its pseudobinary phase diagram, there is a diffusion layer of higher HgTe content built up in the melt near the melt-solid interface which gives a solute concentration gradient in the axial direction. The value of effective diffusion coefficient calculated from fitting of the data to 1D model varies with Hg(1-x)Cd(x)Te growth conditions. This indicates that the growth condition of the Hg(1-x)Cd(x)Te is not purely diffusion controlled. Because of the higher thermal conductivity in the melt than that in the crystal in the growth system, there is a thermal leakage through the fused silica crucible wall near the melt-solid interface. This gives a thermal gradient in the radial direction. Hart, and Thorpe, Hutt and Soulsby have shown that under such conditon a fluid will become convectively unstable as a result of different diffusitivities of temperature and solute. It is quite important to understand the effects of this thermosolute convection on the compositonal segregation in both axial and radial directions in the unidirectionally solidified crystals under various gravitational directions. To reach this goal, we start with a simplified problem to study the effects of thermal-solutal convection on the temperature and solutal fields under various gravitional orientations. We begin by reviewing model governing equations.

Wang, Jai-Ching↗

Effects of depth-dependent thermal expansivity on mantle circulations and lateral thermal anomalies

The influences of depth-dependent thermal expansivity on the structure of Newtonian thermal convection and lateral thermal anomalies are studied. In an aspect-ratio ten box the effects of the depth-dependent expansivity are to produce large aspect-ratio cells with a few relatively stationary upwellings. The lateral thermal anomalies in the lower mantle are greatly diminished by depth-dependent expansivity. This together with a decrease in the temperature derivative of seismic velocities in the lower mantle would support the low level of lateral heterogeneities found in recent tomographic studies.

Hansen, Ulrich↗

On Lateral Viscosity Contrast in the Mantle and the Rheology of Low-Frequency Geodynamics

Mantle-wide heterogeneity is largely controlled by deeply penetrating thermal convective currents. These thermal currents are likely to produce significant lateral variation in rheology, and this can profoundly influence overall material behaviour. How thermally related lateral viscosity variations impact models of glacio-isostatic and tidal deformation is largely unknown. An important step towards model improvement is to quantify, or bound, the actual viscosity variations that characterize the mantle. Simple scaling of viscosity to shear-wave velocity fluctuations yields map-views of long- wavelength viscosity variation. These give a general quantitative description and aid in estimating the depth dependence of rheological heterogeneity throughout the mantle. The upper mantle is probably characterized by two to four orders of magnitude variation (peak-to-peak). Discrepant time-scales for rebounding Holocene shorelines of Hudson Bay and southern Iceland are consistent with this characterization. Results are given in terms of a local average viscosity ratio, (Delta)eta(bar)(sub i), of volumetric concentration, phi(sub i). For the upper mantle deeper than 340 km the following reasonable limits are estimated for (delta)eta(bar) approx. equal 10(exp -2): 0.01 less than or equal to phi less than or equal to 0.15. A spectrum of ratios (Delta)eta(bar)(sub i) less than 0.1 at concentration level eta(sub i) approx. equal 10(exp -6) - 10(exp -1) in the lower mantle implies a spectrum of shorter time-scale deformational response modes for second-degree spherical harmonic deformations of the Earth. Although highly uncertain, this spectrum of spatial variation allows a purely Maxwellian viscoelastic rheology simultaneously to explain all solid tidal dispersion phenomena and long-term rebound-related mantle viscosity. Composite theory of multiphase viscoelastic media is used to demonstrate this effect.

Ivins, Erik R.↗

A Thermally-Conductive Martian Core and Implications for Its Dynamo Cessation

Mars experienced a dynamo process that generated a global magnetic field ~4.3 (or earlier) to 3.6 billion years ago (Ga). The cessation of this dynamo strongly affected Mars’ history and is expected to be linked to thermochemical evolution of Mars’ iron-rich liquid core, which is strongly influenced by its thermal conductivity. Here, we directly measured thermal conductivities of solid iron-sulfur alloys to pressures relevant to the Martian core and temperatures to 1023 Kelvin. Our results show that a Martian core with 16 weight % sulfur has a thermal conductivity of ~19 to 32 Watt meter −1 Kelvin −1 from its top to the center, much higher than previously inferred from electrical resistivity measurements. Our modeled thermal conductivity profile throughout the Martian deep-mantle and core indicates a ~4- to 6-fold discontinuity across the core-mantle boundary. The core’s efficient cooling resulting from the depth-dependent, high conductivity diminishes thermal convection and forms thermal stratification, substantially contributing to cessation of Martian dynamo.

Wen-Pin Hsieh↗

Non-Newtonian Convection and Compositional Buoyancy: Advances in Modeling Convection and Dome Formation on Europa

Numerical modeling of non-Newtonian convection in ice shows that convection controlled by grain boundary sliding rheology may occur in Europa. This modeling confirms that thermal convection alone cannot produce significant dome elevations. Domes may instead be produced by diapirs initiated by thermal convection that in turn induces compositional segregation. Exclusion of impurities from warm upwellings would allow sufficient buoyancy for icy plumes to account for the observed approximately 100 m topography of domes, provided the ice shell has a small effective elastic thickness (approximately 0.2 to 0.5 km) and contains low eutectic-point impurities at the few percent level.

Pappalardo, R. T.↗

Thermo-Chemical Convection in Europa's Icy Shell with Salinity

Europa's icy surface displays numerous pits, uplifts, and chaos terrains that have been suggested to result from solid-state thermal convection in the ice shell, perhaps aided by partial melting. However, numerical simulations of thermal convection show that plumes have insufficient buoyancy to produce surface deformation. Here we present numerical simulations of thermochemical convection to test the hypothesis that convection with salinity can produce Europa's pits and domes. Our simulations show that domes (200-300 m) and pits (300-400 m) comparable to the observations can be produced in an ice shell of 15 km thick with 5-10% compositional density variation if the maximum viscosity is less than 10(exp 18) Pa sec. Additional information is included in the original extended abstract.

Han, L.↗

Laboratory and theoretical models of planetary-scale instabilities and waves

Research work is proceeding in theoretical, numerical, and experimental geophysical fluid dynamics leading up to a reflight of the GFFC (Geophysical Fluid Flow Cell Experiment) on USML-2. The work is intended not only to generate ideas for future space experiments, but to provide fundamental results concerned with nonlinear and chaotic properties of thermal convection and baroclinic waves in terrestrial and planetary atmospheres. The major efforts are focussed on thermal convection in a rapidly rotating annulus relevant to Jovian atmospheric dynamics, and on the chaotic behavior of baroclinic waves relevant to the Earth's atmosphere. The approach, in preparation for USML-2, is primarily theoretical and numerical. Mechanistic process models are solved numerically in order to identify physical mechanisms that may be observed in the GFFC, and which are important in real geophysical applications. The results from numerical simulations of geophysical fluid flow (subject to rotation and stratification) are compared with previous GFFC experiments on Spacelab-3 and with existing and proposed terrestrial laboratory experiments of various types. Pattern recognition algorithms have been employed to generate low-dimensional descriptions of the highly nonlinear and turbulent numerical simulations. Such empirically truncated descriptions provide for simplified but robust physical interpretations of the dynamics, as well as yielding highly efficient computations of these chaotic flows.

Hart, John E.↗

A new approach to the study of the turbulence layer

Turbulent thermal convection is of considerable importance in fluid dynamical transport phenomena occurring, for example, in the planetary boundary layer of the Earth, the interiors of stars, and accretion disks. In particular, during a significant portion of the evolutionary phase of many stars having convectively unstable cores or outer envelopes, a substantial fraction of energy is transported from the central layers to the outer layers by thermal convection. Moreover, as much of the interior of a star is in highly turbulent motion, a complete theory of stellar structure and evolution requires the explicit consideration of turbulence in order to have expressions for the turbulent quantities arising in the stellar structure equations, and particularly, the turbulent fluxes that appear in the total flux conservation equation, such as the convective flux, kinetic energy flux, etc. A reliable quantification of these fluxes continues to present a challenge in astrophysical fluid dynamics, primarily because astrophysical turbulence is almost always fully-developed and nearly inviscid, and therefore governed by strong nonlinear interactions that distribute the energy among a very wide spectrum of eddies with scales ranging from the characteristic dimension of the flow to those sufficiently small to be affected by viscous dissipation. Furthermore, astrophysical flows are invariably compressible, anisotropic, and inhomogeneous, which requires the consideration of the dynamics of longitudinal modes and their interaction with the transverse modes, as well as complicated boundary conditions. In order to reach a compromise between analytical and numerical tractability and the basic physics of turbulent convection, we have constructed a model of stationary turbulent convection that yields various turbulence statistics, including the convective flux, that are required in stellar evolution models.

Levenson, Ruth A.↗

Diffusion in liquid state and solidification of binary system (M-7)

Diffusion is one of the most fundamental physical phenomena. It relates to the manufacturing of almost all materials. Therefore, the precise knowledge of diffusivities of relevant materials is necessary for the optimization of these processes. On the other hand, such knowledge is indispensable to understanding the diffusion mechanism and structure of liquid metal in the field of physical metallurgy. Many diffusion experiments on solid metal were undertaken and a lot of data were accumulated. But on liquid metals there are few measurements because of experimental difficulties, such as thermal convection, induced by very slight temperature gradients in the specimen. Under microgravity conditions, the movement of liquid metal due to density differences and thermal convection must be suppressed markedly. Therefore, the transportation process will be controlled only by the diffusion of constituent atoms. These conditions offer the optimum environments for the diffusion experiment. The experiments are briefly described. Diffusion couples are prepared by attaching end to end two rods of different pure metals using hot press equipment. These couples are inserted into a graphite crucible and then doubly enclosed by two silica ampoules, respectively. The specimen is inserted into a tantalum cartridge, which is welded in a vacuum using an electron-beam apparatus. These cartridges are charged in the continuous heating furnace in space and held at a given temperature for a predetermined time and then solidified. The concentration distribution of elements in these specimens will be measured along the rod axis by means of an electron probe microanalyzer. The counterdiffusivity of the liquid metal binary system is determined on the basis of the compensated concentration distribution profile for thermal contraction.

Dan, T.↗

The dynamical evolution of the protosolar nebula

Evolutionary models for protostellar nebulae are calculated under the hypothesis that the only source for the turbulent viscosity is thermal convection. The viscous stress is approximated by an 'alpha' model, and the constant alpha is calculated in terms of the properties of turbulent thermal convection. A relatively sensitive dependence of the Rosseland mean opacity on temperature is needed for the vertical temperature gradient of the nebula to become convectively unstable. However, this requires that the vertical optical depth in the nebula is relatively sensitive to the total surface density, and as the disk is depleted of matter by protostellar accretion, the Rosseland mean optical depth drops and the disk must become convectively unstable. This limits the amount of mass that the nebula can accretionally process before the convective turbulence ceases. The resulting disk evolutionary properties are calculated and comparisons with the solar system are made.

Ruden, Steven P.↗

Influence of Natural Convection and Thermal Radiation Multi-Component Transport in MOCVD Reactors

The influence of Grashof and Reynolds number in Metal Organic Chemical Vapor (MOCVD) reactors is being investigated under a combined empirical/numerical study. As part of that research, the deposition of Indium Phosphide in an MOCVD reactor is modeled using the computational code CFD-ACE. The model includes the effects of convection, conduction, and radiation as well as multi-component diffusion and multi-step surface/gas phase chemistry. The results of the prediction are compared with experimental data for a commercial reactor and analyzed with respect to the model accuracy.

Lowry, S.↗

Rayleigh-Benard Simulation using Gas-Kinetic BGK Scheme in the Incompressible Limit

In this paper, a gas-kinetic BGK model is constructed for the Rayleigh-Benard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times and pseudo-temperature in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr=1 in the original BGK model. The 2D Rayleigh-Benard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results.

Xu, Kun↗