Showing papers on "Convection published in 1991"

A Scheme for Representing Cumulus Convection in Large-Scale Models

Abstract: Observations of individual convective clouds reveal an extraordinary degree of inhomogeneity, with much of the vertical transport accomplished by subcloud-scale drafts. In view of these observations, a representation of moist convective transports for use in large-scale models is constructed, in which the fundamental entities are these subcloud-scale drafts rather than the clouds themselves. The transport by these small-scale drafts is idealized as follows. Air from the subcloud layer is lifted to each level i between cloud base and the level of neutral buoyancy for undilute air. A fraction (ϵi) of the condensed water is then converted to precipitation, which falls and partially or completely evaporates in an unsaturated downdraft. The remaining cloudy air is then assumed to form a uniform spectrum of mixtures with environmental air at level i; these mixtures ascend or descend according to their buoyancy. The updraft mass fluxes Mi are represented as vertical velocities determined by the amount o...

The Energy Method, Stability, and Nonlinear Convection

Abstract: Introduction*Illustration of the energy method*The Navier-Stokes equations and the Benard problem*Symmetry, Competing Effects, and Coupling Parameters*Convection problems in a half space*Generalized energies and the Lyapunov method*Geophysical problems*Surface tension driven convection*Convection in generalized fluids*Time dependent basic states*Electrohydrodynamic and magnetohydrodynamic convection* Ferrohydrodynamic convection*Reacting viscous fluids*Multi-component convection diffusion*Convection in a compressible fluid*Temperature dependent fluid properties* Penetrative convection*Nonlinear stability in ocean circulation models*Numerical solution of eigenvalue problems*Useful Inequalities*References*Index

Eddy Diffusivity and Countergradient Transport in the Convective Atmospheric Boundary Layer

Abstract: To describe the heat and scalar fluxes in the convective boundary layer, we propose expressions for eddy diffusivities and countergradient terms. The latter expressions can be used in a modified flux-gradient approach, which takes account for nonlocal convective vertical exchange. The results for heat are based on a derivation similar to that of Deardorff by utilizing the turbulent heat-flux equation, but the closure assumptions applied to the heat-flux budgets are different. As a result, the physical interpretation for the countergradient term differs; our countergradient term results from the third-moment transport effect, while Deardorff's results from the buoyancy production term. On the basis of our analysis, we are able to calculate an eddy diffusivity for heat, using large-eddy simulation results. The results are presented in the form of a similarity profile, using the convective velocity scale w* and the inversion height zi. It is shown that the latter profile is well behaved and that it ...

The Depth of the Solar Convection Zone

Abstract: The transition of the temperature gradient between being subadiabatic and adiabatic at the base of the solar convection zone gives rise to a clear signature in the sound speed. Helioseismic measurements of the sound speed therefore permit a determination of the location of the base of the convection zone. Two techniques were tested by applying them to artifical data, obtained by adding simulated noise to frequencies computed from two different solar models. The determinations appear to be relatively insensitive to uncertainties of the physics of the solar interior. From an analysis of observed frequencies of solar oscillation it is concluded that the depth of the solar convection zone is (0.287 + or - 0.003) solar radii.

Apparent tropospheric response to MeV‐GeV particle flux variations: A connection via electrofreezing of supercooled water in high‐level clouds?

Abstract: The ionization production by MeV-GeV particles (mostly galactic cosmic rays) in the lower atmosphere has-well defined variations on a day-to-day time scale related to solar activity, and on the decadal time scale related to the sunspot cycle. New results based on an analysis of 33 years of northern hemisphere meteorological data show clear correlations of winter cyclone intensity (measured as the changes in the area in which vorticity is above a certain threshold) with day-to-day changes in the cosmic ray flux. Similar correlations are also present between winter cyclone intensity, the related storm track latitude shifts, and cosmic ray flux changes on the decadal time scale. These point to a mechanism in which atmospheric electrical processes affect tropospheric thermodynamics, with a requirement for energy amplification by a factor of about 107 and a time scale of hours. A process is hypothesized in which ionization affects the nucleation and/or growth rate of ice crystals in high-level clouds by enhancing the rate of freezing of thermodynamically unstable supercooled water droplets which are known to be present at the tops of high clouds. The electrofreezing increases the flux of ice crystals that can glaciate midlevel clouds. In warm core winter cyclones the consequent release of latent heat intensifies convection and extracts energy from the baroclinic instability to further intensify the cyclone. As a result, the general circulation in winter is affected in a way consistent with observed variations on the interannual/decadal time scale. The effects on particle concentration and size distributions in high-level clouds may also influence circulation via radiative forcing.

Magnetically controlled convection in a paramagnetic fluid

Abstract: CONVECTION in a liquid is important for problems involving heat transfer and crystal growth from a melt. The driving force for convection is usually the density difference between hot and cold regions of the fluid. If the fluid has a magnetic susceptibility that varies with temperature, magnetic forces, rather than buoyancy, can be made to drive convective motion. Studies on ferrofluids (suspensions of ferromagnetic particles1) have shown that magnetic convection can be initiated in a homogeneous magnetic field2,3 and enhanced in a field gradient4. We show here that the strong magnetic fields available from superconducting magnets can be used to induce magnetic convection in normal paramagnetic fluids, such as solutions of paramagnetic salts or melts of paramagnetic solids. We have used a magnetic field both to enhance and to suppress buoyancy-driven convection in a solution of gadolinium nitrate, the sign of the effect depending on the relative orientation of magnetic-field and temperature gradients. The effect might be exploited in heat-transfer devices or to control microstructures in crystal growth.

Natural convection in a mushy layer

Abstract: Governing equations for a mushy layer are analysed in the asymptotic regime Rm [Gt ] 1, where Rm is an appropriately defined Rayleigh number. A model is proposed in which there is downward flow everywhere in the mushy layer except in and near localized chimneys, which are characterized by having zero solid fraction. Upward, convective flow within the chimneys is driven by compositional buoyancy. The radius of each chimney is determined locally by thermal balances within a boundary layer that surrounds it. Simple solutions are derived to determine the structure of the mushy layer away from the immediate vicinity of chimneys in order to demonstrate the gross effects of convection upon the solidification within the layer.

Turbulent Compressible Convection

Abstract: Numerical simulations with high spatial resolution (up to 96-cubed gridpoints) are used to study three-dimensional, compressible convection. A sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent. 39 refs.

Heating solar coronal holes

Abstract: It has been shown that the coronal hole, and the associated high-speed stream in the solar wind, are powered by a heat input of the order of 500,000 ergs/sq cm s, with most of the heat injected in the first 1-2 solar radii, and perhaps 100,000 ergs/sq cm s introduced at distances of several solar radii to provide the high speed of the issuing solar wind. The traditional view has been that this energy is obtained from Alfven waves generated in the subphotospheric convection, which dissipate as they propagate outward, converting the wave energy into heat. This paper reviews the generation of waves and the known wave dissipation mechanisms, to show that the necessary Alfven waves are not produced under the conditions presently understood to exist in the sun, nor would such waves dissipate significantly in the first 1-2 solar radii if they existed. Wave dissipation occurs only over distances of the order of 5 solar radii or more.

Observations with Moored Acoustic Doppler Current Profilers in the Convection Regime in the Golfe du Lion

Abstract: In the Golfe du Lion, south of France, favorable conditions for deep winter convection exist and were documented by the MEDOC experiments during 1969–75. A renewed investigation of that regime with upward-looking moored acoustic Doppler current profilers (ADCPs) was carried out during 24 January–5 March 1987, to record the three-dimensional currents associated with the deep mixing. While in the earlier studies initial deep convection did not begin until fairly late in the winter season, a very strong Mistral around 10 January 1987 had already generated a 1arge deep-mixed patch, homogeneous down to around 2000 m at deployment time. Three ADCPs, two working at 150 kHz and one at 75 kHz, were moored in a triangle of 15 km sidelength at 550–780 m depth. Full records at 1-hour ensemble time intervals, 400 pings per ensemble, 8 m bin lengths were obtained by the 75 kHz and one of the 150 kHz ADCPs. In mid-February, a second Mistral hit the region. With the onset of strong winds and surface cooling the ...

Convection in three dimensions with surface plates: Generation of toroidal flow

Abstract: This work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics. The model is three-dimensional and includes surface plates; it allows plate velocity to change dynamically according to the forces which result from convection. It is shown that plates are an effective means of introducing a toroidal component into the flow field. After initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimize the toroidal flow field. The toroidal field decays with depth from its value at the surface; the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries. Layered viscosity increasing with depth causes the toroidal field to decay more rapidly, effectively confining it to the upper, low-viscosity layer. The effect of viscosity layering on the poloidal field is relatively small, which is attributed to its generation by temperature variations distributed throughout the system. The generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the earth. A low-viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle. The resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles.

Heat Transfer with Freezing and Thawing

Abstract: 1. BASIC EQUATIONS . The Nature of the Thermodynamic System. General Energy Equation for a Continuum. Energy Balance at the Phase-Change Interface. Nonlinearity of Solidification Problems. Conservation of Mass, Momentum and Energy for Continuum. Heat, Mass, and Momentum Flow in Porous Media. Nomenclature. References. 2. PLANE PROBLEMS WITH TEMPERATURE BOUNDARY CONDITIONS. Neumann Problem and Variations. Neumann Problem With Variable Properties. Neumann Problem With Variable Temperatures. Melting Temperature Range. Subcooled Liquid - Frazil Ice. Solidification in Contact with Cold Wall. Thaw With Consolidation of Melted Medium. Freeze of a Flowing Fluid. Freeze Coating on a Moving Sheet. Continuous Casting of Slab. Convective Effects. Nomenclature. References. 3. PLANE PROBLEMS WITH CONVECTION (RADIATION) AT FREE SURFACE. Single-Phase Problems. Two-Phase Problems. Nomenclature. References. 4. PLANE PROBLEMS WITH SPECIFIED SURFACE HEAT FLUX. Exact Solution for Semi-Infinite Medium. Approximate Solutions, Single Phase, Semi-Infinite Region. Two-Phase Problems. Ablation with Complete Removal of Melt. Freezing of a Flowing Fluid. Nomenclature. References. 5. THAW BENEATH INSULATED STRUCTURES QUASI-STEADY SOLUTIONS. General Quasi-Steady Relations. Nomenclature. References. 6. CYLINDRICAL PROBLEMS . Outward Phase Change, Infinite Domain. Outward Phase Change, Finite Geometry. Inward Phase Change. Convective Effects and Relations. Nomenclature. References. 7. PROBLEMS IN SPHERICAL GEOMETRY. Outward Phase Change. Spherical Problems, Inward Growth. Nomenclature. References. 8. PHASE CHANGE IN POROUS MEDIA. Natural Convection in Porous Media Without Phase Change. Natural Convection With Phase Change. Coupled Energy and Mass Fluxes. Nomenclature. References. APPENDIX A: Quasi-Static Approximations and Perturbation Methods. APPENDIX B: The Heat Balance Integral Method. APPENDIX C: Biot's Variational Principle. APPENDIX D: Error Function and Error Integral Family. APPENDIX E: Exponential Integral and Related Functions. APPENDIX F: Porous Media and Macroscopic Equations. APPENDIX G: Laplace Transforms and Phase-Change Problems. SUBJECT INDEX. AUTHOR INDEX.

Effects of rotation on convective turbulence

Abstract: Laboratory experiments were carried out to investigate the effects of rotation on turbulent convection. The experimental facility was a bottom-heated, water-filled, cubical tank mounted on a turntable. The investigations were performed over a wide range of bottom buoyancy fluxes q0 and rotation rates Ω, including Ω = 0; q0 and Ω were held constant during each experiment. The depth of the water column H was fixed for the entire experimental programme. For the non-rotating experiments, the r.m.s. velocity fluctuations were found to scale well with the convective velocity , where the integral lengthscale is estimated as lr ≈ 0.25hc. The mean buoyancy gradient in the mixed layer was found to be much higher than in the corresponding non-rotating case, and the r.m.s. fluctuations and mean buoyancies were found to scale satisfactorily with (q0Ω)½. A spectral form for the temperature fluctuations in rotating convection is also proposed and is compared to the experimental results.

Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity

Abstract: Numerical calculations are presented for the steady three-dimensional structure of thermal convection of a fluid with strongly temperature-dependent viscosity in a bottom-heated rectangular box. Viscosity is assumed to depend on temperature T as exp ( --ET), where E is a constant ; viscosity variations across the box r (= exp (E)) as large as lo5 are considered. A stagnant layer or lid of highly viscous fluid develops in the uppermost coldest part of the top cold thermal boundary layer when r > rcl, where r = rcl = 1.18 x 103R,0~308 andR, is the Rayleigh number based on the viscosity at the top boundary. Three-dimensional convection occurs in a rectangular pattern beneath this stagnant lid. The planform consists of hot upwelling plumes at or near the centre of a rectangle, sheets of cold sinking fluid on the four sides, and cold sinking plume concentrations immersed in the sheets. A stagnant lid does not develop, i.e. convection involves all of the fluid in the box when r rc2 = 3.84 x 106R;1.36. The planform of the convection is rectangular with the coldest parts of the sinking fluid and the hottest part of the upwelling fluid occurring as plumes at the four corners and at the centre of the rectangle, respectively. Both hot uprising plumes and cold sinking plumes have sheet-like extensions, which become more well-developed as r increases. The whole-layer mode of convection occurs as two-dimensional rolls when r < min (rcl, rc2). The Nusselt number Nu depends on the viscosity at the top surface more strongly in the regime of whole-layer convection than in the regime of stagnant-lid convection. In the whole-layer convective regime, Nu depends more strongly on the viscosity at the top surface than on the viscosity at the bottom boundary.

3‐D Convection With Variable Viscosity

Abstract: Accepted 1990 September 6. Received 1990 July 16; in original form 1990 May 3 SUMMARY report numerical calculations for 3-D convection with variable viscosity. A hybrid spectral and finite difference method is used. The coupling of modes in the equation of motion, which is caused by lateral viscosity variations, is treated iteratively. Solutions for bimodal, hexagonal, square, triangular and spoke patterns are reported for bottom heated convection at infinite Prandtl number. The Rayleigh number, based on the viscosity at the mean of top and bottom temperature, is between critical and lo5, and temperature-induced viscosity contrasts up to 100 are considered (lo00 in one case). In agreement with results from laboratory experiments we find that at low Rayleigh number temperature-dependent viscosity favours flow patterns like squares or hexagons, where a columnar rising current is surrounded by sheet-like descending flow. The dichotomy in geometry between upwelling and sinking flow becomes more pronounced with increasing viscosity contrast. The temperature dependence of viscosity gives rise to a toroidal velocity component; however, it amounts only to a few per cent of the total velocity. In contrast, at the earth’s surface an approximate equipartitioning of poloidal and toroidal energy is found. We show that with non-Newtonian and depth-dependent rheology the toroidal component at the free surface can become significant, and a pattern reminiscent of plate motion can arise in a free convection model. Although these results are obtained in a parameter range which is not directly applicable to the earth, they support the conclusions that (i) upwelling flow in the mantle is unlikely to be sheet-like and will probably be in the form of columnar plumes, and that (ii) the toroidal motion found at the earth’s surface is due to the highly non-linear rheology which leads to the existence of mobile surface plates and is not caused by viscosity variations related to lateral temperature contrasts deeper in the mantle.

Experimental study of directional solidification of aqueous ammonium chloride solution

Abstract: Directional solidification experiments have been carried out using the analog casting system of NH4Cl-H2O solution by cooling it from below with a constant-temperature surface ranging from -31.5 C to +11.9 C. The NH4Cl concentration was 26 percent in all solutions, with a liquidus temperature of 15 C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as +11.0 C. However, when the bottom temperature was raised to +11.9 C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250.

A New Hue Capturing Technique for the Quantitative Interpretation of Liquid Crystal Images Used in Convective Heat Transfer Studies

Abstract: A new image processing based color capturing technique for the quantitative interpretation of liquid crystal images used in convective heat transfer studies is presented. This method is highly applicable to the surfaces exposed to convective heating in gas turbine engines. It is shown that, in the single-crystal mode, many of the colors appearing on the heat transfer surface correlate strongly with the local temperature. A very accurate quantitative approach using an experimentally determined linear hue vs temperature relation is found to be possible. The new hue-capturing process is discussed in terms of the strength of the light source illuminating the heat transfer surface, the effect of the orientation of the illuminating source with respect to the surface, crystal layer uniformity, and the repeatability of the process. The present method is more advantageous than the multiple filter method because of its ability to generate many isotherms simultaneously from a single-crystal image at a high resolution in a very time-efficient manner.

A Three-Dimensional Numerical Study of Deep-Water Formation in the Northwestern Mediterranean Sea

Abstract: Deep-water formation (DWF) in the northwestern Mediterranean Sea and the subsequent horizontal circulation are investigated in a rectangular basin with a three-dimensional primitive equation model. The basin is forced by constant climatological heat and salt fluxes. Convective motion is parameterized by a simple nonpenetrative convective adjustment process plus Richardson number–dependent vertical eddy viscosity and diffusivity. A homogeneous column of dense water is progressively formed in the forcing area. Meanders of 40-km wavelength develop at the periphery of the column. These features agree with observations. Energy studies show that the meanders are generated mainly through a baroclinic instability process. These meanders, and the associated cells of vertical motion, contribute to the process of DWF. They generate vertical advection, while the associated horizontal advection tends to restratify the surface water of the column, and thus to inhibit very deep convection. Just before the end o...

A model evaluation of noninductive graupel‐ice charging in the early electrification of a mountain thunderstorm

Abstract: The role of noninductive graupel-ice charge separation in the early electrification of the July 31, 1984, New Mexico mountain thunderstorm is assessed with a three-dimensional kinematic cloud model along with multiple Doppler radar and in situ measurements. Observations of the early electrification rate and the electric field distribution are consistent with modeled values that result when the noninductive mechanism works under the influence of convective motions and precipitation growth. An increase in ice particle concentrations and sizes, arising from vigorous precipitation growth, accelerates graupel-ice collision rates and hence the noninductive charging rate. Growing graupel particles experience increasing fall speed as they rise toward the top of the updraft. The resulting vertical flux convergence of graupel containing charge from previous noninductive collisions is a significant factor in the growth of the main negative charge density. This implies that a combination of air motion, precipitation interaction, and sedimentation contributes to the rapid intensification of storm electric fields. The linear electrification phase, which begins with the cessation of convective growth, is caused by a roughly constant noninductive charging rate and by the separation of negatively charged graupel and positively charged smaller ice particles by differential sedimentation, downdrafts, and horizontal advection in vertically sheared flow. When the sign reversal temperature for noninductive charging is assumed to be −10°C, the model results are characterized by a main negative charge in middle levels and provide the best overall agreement with the in situ field measurements in the July 31 storm. For a sign reversal temperature of −21°C the model results are characterized by a main positive charge center in middle levels, and the electric field polarity is opposite to the polarity measured at low and middle levels of the storm. The model and observational data, combined with findings of some laboratory studies, support the hypothesis that the actual reversal temperature in the July 31 storm is around −10°C. When the model includes the inductive graupel-droplet charging mechanism in addition to the noninductive mechanism, the effect of inductive charging is secondary to that of noninductive charging. The net effect of adding induction is dissipative. For example, the maximum field strength at the location of the aircraft measurements is slightly less than in the case where the noninductive mechanism acts alone. Weak charge screening layers were found to develop on the boundary of the modeled cloud.

The pulsations of ZZ Ceti stars – III. The driving mechanism

Abstract: The outer layers of the variable white dwarfs are in a state of partial ionization. During the pulsation cycle the base of the ionization zone is strongly heated by the radiative layers below, in phase with the pressure perturbation. If this excess heat is not quickly lost at the surface, then the driving effect is strong. The surface flux perturbation tends to be small and delayed in phase because the surface flux is remarkably insensitive to temperature changes in the deeper layers of the ionization zone. This insensitivity is closely associated with the well known inward divergence of the solutions for the equilibrium thermal structure in the convective layers. The mechanism which excites the oscillations could be called convective driving

Turbulent Alfven boundary layer in the polar ionosphere: 1. Excitation conditions and energetics

Abstract: Instability of laminar magnetospheric convection with respect to the strongly anisotropic Alfven waves which are of small scale in the horizontal plane is examined. The waves prove to be trapped in the ionospheric Alfven resonator, bounded from below by the ionospheric E layer and from above by a zone of rapidly increasing Alfven velocity at altitudes of up to ∼104 km. The finite-amplitude Alfven waves dissipate within a layer of anomalous resistance formed near the upper wall of the resonator. As a result, a high-energy particle source appears in the upper ionosphere. Further evolution results in the transition of laminar convection to turbulent flow conditions and in the formation of a turbulent Alfven boundary layer in the polar ionosphere at altitudes from 10² to 104 km. The energy status of the turbulent Alfven boundary layer is calculated. It has been shown that the accelerated-electron energy flux density can reach ∼100 ergs cm−2 s−1.

Transitions between patterns in thermal convection.

Abstract: We present experimental studies of the transitions between conduction, hexagons, and rolls in non-Boussinesq convection of gaseous ${\mathrm{CO}}_{2}$ in a cylindrical cell of radius-to-height ratio 86. Except for the transition from conduction to hexagons, transitions occur when the two states involved have nearly the same value of a generalized potential rather than at the stability limits. Conduction gives way to hexagons via the propagation of a front connecting the two states, while the transitions between hexagons and rolls are facilitated at the cell walls which appear to nucleate the minority state.

Natural convection in the subarctic snow cover

Abstract: The purpose of this study was to determine if air convects in a natural snow cover. To detect convection, the temperature field in the subarctic snow cover in Fairbanks, Alaska, was measured hourly during three winters (1984–1987) using an array of thermistors which were suspended on threads and allowed to be buried by snowfall. The results indicate that convection occurred sporadically in 1984–1985 and almost continuously in 1985–1986 and 1986–1987. The evidence was (1) simultaneous warming and cooling at different locations in a horizontal plane in the snow, and (2) horizontal temperature gradients of up to 16°C m−1 During the winter, warm and cold zones developed in the snow and remained relatively fixed in space. We interpret these zones to be the result of a diffuse plumelike convection pattern linked to spatial variations in the temperature of the snow-soil interface. Air flow was inferred to have been primarily horizontal near the base of the snow and vertical elsewhere. Calculated flow speeds were of the order of 0.2 mm s−1, with a maximum value of 2 mm s−1 The convective circulation was time-dependent, with perturbations such as high wind or rapid changes in air temperature triggering periods when horizontal temperature gradients were strongest, suggesting that these were also periods when the air flow was fastest. The coincidence of depth hoar crystals with horizontal c axes and the horizontal flow lines at the base of the snow suggests that convection may have affected crystal growth directions.

Measurements of sensible and latent heat flux in the western equatorial Pacific Ocean

Abstract: Micrometeorological measurements, including direct eddy-correlation measurements of heat and moisture fluxes, have been made from shipboard under light-wind conditions in the western equatorial Pacific warm pool. Air-sea temperature differences were typically 1.5°–2°C, that is, 1°–1.5°C larger than long-term averages from merchant ship data. A sea surface “cool skin” of about 0.3°C was observed. Bulk transfer coefficients for both fluxes agree well with the predictions of Liu et al. (1979) in the convective wind speed regime below 4 m s−1. Between 4 and 6 m s−1 values of the neutral exchange coefficients were CEN - 0.89 × 10−3; CHN = 1.03 × 10−3; CDN = 1.16 × 10−3. At zero mean wind speed, latent heat flux is maintained at about 25 W m−2 by convective exchange. Inertial dissipation estimates of the latent heat flux are about 20% lower than the directly measured eddy-correlation values below 4 m s−1.

Toroidal-Poloidal Partitioning of Lithospheric Plate Motions

Abstract: A spherical harmonic expansion of tectonic plate motions on the Earth requires both poloidal and toroidal harmonics. Each spectrum decays fairly uniformly as l-2 (l is the spherical harmonic degree), and the toroidal-poloidal ratio of the degree power is between 0.5 and 1.0 for all degrees up to 128. Convection in a laterally homogeneous medium will excite only poloidal motions; hence the question of why the toroidal component of plate motion is so large. Numerical models of 3-D convection with surface plates show that the rheological heterogeneity represented by plate boundaries can account for the excitation of toroidal surface motions from an underlying poloidal convective flow. Plates also account for the l-2 decay of the spectra, which is a simple geometric consequence of the plate-like velocity field. Lateral viscosity variations can also account for the net rotation of the lithosphere in the hot spot reference frame; this requires order of magnitude lateral viscosity variations. The spectra of plate motions depends on the geometries of the plates as well as their relative motions. A Monte Carlo simulation of plate motions shows that the observed toroidal-poloidal ratio for all degrees is less than would be expected for most plate motions, given the existing geometry. Relatively simple numerical models of 3-D convection with surface plates evolve to a final steady state (when it exists) that minimizes the toroidal-poloidal ratio of plate motion. This suggests that the much more complex system of plates on the Earth may be similarly governed.

Convection transfer system

Abstract: A system provides convective transfer from a workpiece (10) to a flowing fluid. A gap (16) is formed between the workpiece (10) and a facesheet (12) containing fluid supply nozzles (18) and fluid return nozzles (20). The fluid is fed to the supply nozzles (18), travels a short distance within the gap (16) adjacent to the facesheet (12), and exits via return nozzles (20). The flow cross section and flow density facilitate heat transfer at a moderate flow rate and low fluid pressure. The system is also applicable for chemical transfer such as plating or etching printed circuit boards and for transfer through a semi-permeable membrane.

A high‐latitude, low‐latitude boundary layer model of the convection current system

Abstract: Observations suggest that both the high- and low-latitude boundary layers contribute to magnetospheric convection, and that their contributions are linked. In the interpretation pursued here, the high-latitude boundary layer (HBL) generates the voltage while the low-latitude boundary layer (LBL) generates the current for the part of the convection electric circuit that closes through the ionosphere. However, the interpretation has a self-consistency problem: in their magnetospheric settings, the two boundary layer generators are ostensibly independent, but in the ionosphere, Ohm's law ties the voltage to the current, and, thereby, couples them. This paper gives a model that joins the high- and low-latitude boundary layers consistently with the ionospheric Ohm's law. It describes an electric circuit linking both boundary layers, the region 1 Birkeland currents, and the ionospheric Pedersen closure currents. The model works by using the convection electric field that the ionosphere receives from the HBL to determine two boundary conditions to the equations that govern viscous LBL'ionosphere coupling. The result provides the needed self-consistent coupling between the two boundary layers and fully specifies the solution for the viscous LBL-ionosphere coupling equations. The solution shows that in providing the current required by the ionospheric Ohm's law, the LBL needs only a tenth of the voltage that spans the HBL. (This has led to undervaluing the LBL's role in convection.) The solution also gives the latitude profiles of the ionospheric electric field, parallel currents, and parallel potential. The parallel currents span the convection reversal and shift both north and south relative to the polar cap boundary as the strength of the transpolar potential changes, offering an empirical test of the model. It predicts that the plasma in the inner part of the LBL moves sunward instead of antisunward and that, as the transpolar potential decreases below about 40 kV, reverse polarity (region 0) currents appear at the poleward border of the region 1 currents. A possible problem with the model is its prediction of a thin boundary layer (∼1000 km), whereas thicknesses inferred from satellite data tend to be greater.

Non-Darcy Mixed Convection Along a Vertical Wall in a Saturated Porous Medium

Abstract: In most of the previous studies of either natural or mixed convection, the boundary-layer formulation of Darcy's law and the energy equation were used. However, the inertial effect is expected to become very significant when the pore Reynolds number is large. This is especially true for the case of either the high Rayleigh number regime or for high-porosity media. In spite of its importance in many applications, the non-Darcy flow effect has not received much attention. In this note, non-Darcy flow effects, which include the inertial and thermal dispersion effects, are closely examined. Steady-state non-Darcy convection, in the form of natural, mixed, and forced convection, is considered for a heated vertical surface embedded in a saturated porous medium.

Unsteady mixed convection flow in stagnation region adjacent to a vertical surface

Abstract: The unsteady two-dimensional laminar mixed convection flow in the stagnation region of a vertical surface has been studied where the buoyancy forces are due to both the temperature and concentration gradients. The unsteadiness in the flow and temperature fields is caused by the time-dependent free stream velocity. Both arbitrary wall temperature and concentration, and arbitrary surface heat and mass flux variations have been considered. The Navier-Stokes equations, the energy equation and the concentration equation, which are coupled nonlinear partial differential equations with three independent variables, have been reduced to a set of nonlinear ordinary differential equations. The analysis has also been done using boundary layer approximations and the difference between the solutions has been discussed. The governing ordinary differential equations for buoyancy assisting and buoyancy opposing regions have been solved numerically using a shooting method. The skin friction, heat transfer and mass transfer coefficients increase with the buoyancy parameter. However, the skin friction coefficient increases with the parameter λ, which represents the unsteadiness in the free stream velocity, but the heat and mass transfer coefficients decrease. In the case of buoyancy opposed flow, the solution does not exist beyond a certain critical value of the buoyancy parameter. Also, for a certain range of the buoyancy parameter dual solutions exist.