Theory Of Convection Research Articles

Quasi‐static magnetospheric MHD processes and the “ground state” of the magnetosphere

From the viewpoint of magnetic equilibrium and convection theories, we discuss whether there exists a theoretically well‐defined ground state of the Earth's magnetosphere. As a basis for this discussion, we review the quasi‐static MHD theory and show in a two‐dimensional (2‐D) model that the convecting magnetosphere can (mathematically) reach a steady state. The steady state configuration has fairly stretched magnetotail field lines and is, therefore, likely to be unstable to the tearing mode instability which ultimately leads to substorm onset in magnetotail regions with stretched field lines. We present an interpretation of the substorm phenomenon in terms of sequences of quasi‐static MHD equilibrium states and argue that, under the influence of convection, magnetic substorms occur periodically in Earth's magnetosphere, thus being an integral part of the entire convection cycle. After explosively releasing plasma and magnetic field energies in a substorm, the magnetosphere starts the convection process again from a low‐energy state. In addition to “smooth” tail field configurations, there exist oscillatory equilibrium tail structures with lower potential energy.We discuss the concept of the ground state of the magnetosphere within the context of 2‐D quasi‐static MHD models for the near‐Earth magnetosphere. However, we are unable to find a definition of a single magnetospheric ground state that is conceptually simple and computationally feasible. The term “ground state” denotes the lowest energy state of a system, which for a magnetosphere in quasi‐static force equilibrium is the empty vacuum magnetic field configuration with zero thermal plasma pressure. The real magnetosphere never approaches that state. Therefore we propose the term “average magnetosphere” for defining a baseline configuration that corresponds to average solar wind conditions. Earth's magnetosphere is convectively driven and powered by the solar wind. Thus all potential energy states W = ∫ [P/(γ − 1) + B²/2µ0] dV that belong to a particular convection time sequence between substorm events are transient in time. Therefore the newly defined “average magnetosphere” has a potential energy 〈W − Wvacuum〉 representing the time average of equilibrium states over the substorm cycle. Thus a “quiet” magnetosphere would have a net potential energy lower than the average, whereas an “active” magnetosphere would have a higher energy. It is an unresolved theoretical problem, however, to determine the lowest and highest possible energy states for the magnetosphere that are compatible with the thermodynamic condition of quasi‐static convection.Three‐dimensional (3‐D) magnetospheric equilibria have not been computed yet, but we describe our experience with Stern's stretch transformations and a magnetofrictional method for calculating 3‐D magnetospheric MHD equilibria.

Deposition of oral streptococci and polystyrene latices onto glass in a parallel plate flow cell

Deposition of oral bacteria onto glass from a potassium phosphate buffered suspension has been studied in a parallel plate flow cell. Three bacterial strains with known surface free energies and zeta potentials, and two Strains (S. salivarius HB and S. salivarius HB‐C12) having well‐defined surface appendages have been employed. Polystyrene latices were included to provide a comparison with inert particles. Initial deposition rates of the various bacteria ranged from 0–1—2·9 × 103 particles cm “"2 sec”; ‘. The initial deposition rates have been related to an approximate theory of convective diffusion in which electrostatic interactions are omitted. A theory describing the influence of particle desorption and blocking on the deposition rate has been tested for its applicability to bacterial deposition at later stages. From the results it is concluded that a simple convective diffusion theory overestimates the experimental results, due to an increase in hydrodynamic friction of particles closely approaching the surface, which overbalances the attractive van der Waals forces. Deposition at later stages corresponded with theoretical expectations, from which a constant blocking of available adhesion sites on the surface can be concluded. Comparison of the deposition rates of particles experiencing an electrostatic potential barrier while approaching the substratum surface with those experiencing a net attractive force suggests that appendages present on the bacterial cell surface assist in deposition. Desorption is observed only during the first 5–10 seconds after deposition.

Plume Dispersion in the Convective Boundary Layer. Part I: CONDORS Field Experiment and Example Measurements

Abstract Project CONDORS (CONvective Diffusion Observed by Remote Sensors) measured the dispersion of a nonbuoyant plume in the highly convective boundary layer. Laboratory and numerical models have predicted vertical profiles of a passive tracer that are significantly non-Gaussian in shape in convective conditions. However, adequate field data to verify the model results were not available before CONDORS. A lidar measured the three-dimensional distribution of oil fog, and a radar similarly observed a plume of microwave-scattering chaff. The instrumentation, experimental methodology, and data reduction techniques are described. Analysis is still in progress but preliminary results support most of the simulations, including the deviations of vertical profiles from Gaussian model predictions. The experiment centered around the 300 m instrumented tower of the Boulder Atmospheric Observatory. The parameters in convective scaling theory were determined, and extensive information on wind statistics was gathered...

A new look at the causes and consequences of the Icelandic hot-spot

Summary New support for the hypothesis of a lower mantle plume rising near Iceland comes from recent developments in the theory of whole-mantle convection and is inferred from the large heat input required to support the major topographic swell which affects much of the N Atlantic and Greenland. The associated geoid and gravity highs are interpreted as due partly to the swell and its deep compensation and partly to the pressure anomaly caused by the plume. Rapid lateral migration of partially fused material from the plume in the asthenosphere prior to continental break-up caused the early Tertiary volcanism, with subsequent igneous activity concentrated at the ridge crest to form the Icelandic transverse ridge. Progressive expansion of the upper mantle thermal anomaly in response to pressure, in association with the complexities of plate evolution in this region, may account for the early uplift of S Greenland and later uplift of the Blosseville Kyst region. The low density upper mantle would also be expected to give rise to an anomalously high ridge-push force.

On a bounded solution to a pair of coupled nonlinear ordinary differential equations

We present a bounded, decaying solution to a pair of coupled, nonlinear second-order ordinary differential equations arising in the theory of natural convection. The solution is found by transforming the problem into a non-autonomous system in the phase-plane. A uniqueness proof is given for the bounded solution.

Linear and weakly nonlinear problems of the theory of thermal convection in the Earth's mantle

The thermoconvective instability of the upper thermal boundary layer formed by the large-scale convection of the mantle is analysed. The creep in the mantle is assumed transient when strains are small. The linear hereditary medium is accepted as a rheological model which describes the mantle's transient creep. At this rheology the instability is oscillatory and the supercriticality, as suggested by the postglacial rebound data, is small. The application of nonlinear stability theory permits derivation of an asymptotic solution in the form of a steady convective oscillation the amplitude of which is independent of the initial conditions. The supercriticality is considered as a small parameter and perturbation methods are used. The amplitude and the frequency of oscillation are found as functions of the supercriticality.

The influence of a modified mixing-length theory and of an adopted description of the atmosphere on the solar five-minute oscillations

The influence of the modified treatment of subphotospheric convection, as recommended by Deupree (1979) and by Deupree and Varner (1980), on the frequencies of solar five-minute oscillations of degree 1 = 1–100 is studied. As compared with the results for a standard solar model, the convection theory modification has practically no effect on the frequencies near the low frequency edge of the observational interval (at ν ⋍ 2000 μHz), but causes a frequency decrease for high overtones; the effect is larger at larger frequencies. At ν ⋍ 4000 μHz the frequency decrease is about 4–6 μHz for all 1 ≤ 40 and about 8–10 μHz for 1 ⋍ 60–100. If, additionally, we use the dependence T(τ) according to Holweger and Müller (1974) instead of the HSRA model, the joint effect is 1.5–2 times larger. In this case the slope of the theoretical curves in “echelle diagrams” turns out to be in agreement with the observational one for 1 ≤ 20, but the frequencies themselves are approximately 10 μHz lower than those from observations.

マントル対流論の現状

I review the recent topics of the mantle convection, especially with regard to the scales of mantle flows. The studies of 3-D velocity structure of the earth's mantle, geoid, gravity and isotope geochemistry provide a new perspective of the flow in the mantle. Several workers show a clear correlation between the distribution of hotspots and the geoid anomalies obtained by subtracting the contribution of the subducted slabs. Assuming a spherically symmetric viscous earth, several researchers could constrain the form of mantle flow and viscosity structure in the earth by correlating the calculated geoid with the observed one. Seismological studies suggest the existence of aseismic slab beneath 650km discontinuity. If this is a case, the aseismic slab may be explained by several ways on the basis of convection theories, that is, whole mantle convection, layered convection with thermal coupling and the penetrative convection. 3-D velocity structure obtained by several workers show the correlation between the geoid and lower mantle heterogeneity at low degrees (l=2-3) and this correlation was explained by the flow models. Possible seismological indicators of mantle layering are proposed. Seismic anisotropy found by the studies of the long period surface wave correlates with some mantle flow model and may suggest the flow direction or stress field in the real earth. The topography of core-mantle boundary revealed by recent seismological and geodetic studies may constrain the viscosity and thermal properties of mantle near CMB. The heterogeneity in the CMB may be closely related to the dynamics near CMB, for example, entrainment of dense material by the convection and the double diffusive convection. Isotope geochemistry shows that there are many geochemical source regions which have various sizes and age distrbution. Convective mixing was investigated and two opposite views have been presented. In one view, the convection is strong enough to homogenize the geochemical heterogeneities within a geologically short time; in another, both small and large scale heterogeneities persist for 1-2 b. y. The studies mentioned above are combined into the flow models by several workers.

Voyager 2 plasma ion observations in the magnetosphere of Uranus

Positive ion measurements in the magnetosphere of Uranus have been made by the Voyager 2 plasma science experiment. We present an overview of the entire data set and a detailed analysis of the observations from the inner magnetosphere which complements and extends results reported elsewhere. Densities and temperatures are obtained from an analysis which incorporates details of the instrumental response. These results are then used to calculate flux tube particle and energy content to support the hypothesis that the plasma transport is controlled by a solar wind‐driven magnetospheric convection system. Variations in the flux tube content suggest both a local source of plasma, produced from the neutral hydrogen corona of Uranus, and a nonlocal source, convected inward and heated by adiabatic compression. In each case a proton composition is inferred. Sharp boundaries in the high‐energy (approximately 1 keV) plasma population are interpreted in terms of the spatial extent of the magnetospheric convection, with significant shielding of the convection electric field. The convection theory is also used in a simulation of the low‐energy (approximately 10 eV) ion component using the neutral hydrogen source, resulting in distribution functions which qualitatively agree with the observations.

Interacting steady states in thermohaline convection.

We consider the Boussinesq theory for convection in a rectangular box with imposed constant, negative, vertical heat and salt gradients. We analyze the bifurcation of two-dimensional convection steady states near a double instability point defined by a critical value of the thermal Rayleigh number and geometrical aspect ratio. We find that for thermohaline convection the interaction of the two lowest pure-mode steady states does not produce the tertiary bifurcation of periodic solutions because the direction of bifurcation of the modes is always the same, either both supercritical or subcritical. On the other hand, we find that the interaction can produce the secondary bifurcation of mixed-mode steady states, and that jump transitions between multiple, stable, pure-mode steady states are possible. We also find that the mixed-mode steady state is always unstable in the parameter ranges considered.

THE SOLAR-STELLAR CONNECTION - SOLAR STUDIES

ABSTRACT The minimal set of processes which must be added to the standard solar model in order to produce a model that is compatible with all observations which have been properly validated to date is investigated. The global observations which are incompatible with, or not addressed by, the standard model are listed. It is argued that rotation, magnetic fields, and an improved theory of convection are the minimal additional considerations required. Current efforts to accomplish the model upgrading are described, and some future observational programs which are expected to have major impacts on understanding of the solar interior are discussed.

Surface renewal theory for turbulent mixed convection in vertical ducts

A heat transfer correlation for opposing mixed turbulent convection in vertical ducts was obtained utilizing surface renewal theory. The correlation was found to be Nu D b = 0.0115 Re D h 0.8 Pr 0.5 1 + [1 − 696 Re 0.8 D h + 8300 Gr D b Re 2.6 D h (Pr 0.5+1) ] 0.39 The correlation fit data to within 7% over a parameter range of 0.7 < Pr < 7, 1 × 10 4 < Re D h < 2 × 10 4, and 1 × 10 6 < Gr D h < 2 × 10 9. The mean residence time, characterizing the time a clump of fluid resides on the wall, was found to decrease as both Gr D b Re 2.6 D h (Pr 0.5+1) and Re D h increase. This explains the enhanced heat transfer due to buoyancy in opposing mixed turbulent flows. This heat transfer enhancement was also reflected in a decreasing thermal boundary layer thickness with increasing Re D h , Gr D h or Pr.

A Theory for Nonprecipitating Moist Convection between Two Parallel Plates. Part I: Thermodynamics and “Linear” Solutions

A defining feature of moist convection is latent heating. A simple, mathematically tractable but thermody-namically reasonable Kuo-type model is developed to isolate some important effects of latent heating on the structure and organization of moist convection. Convection in a shallow, unsheared layer of viscous moist air between two rigid horizontal plates is examined. Unlike previous analytical work, a realistic thermodynamic equation is used, based on the assumption that no precipitation falls out of saturated air. This assumption isolates reversible latent heating from the complicating effects of precipitation. The crucial step is to express the buoyancy of moist air as a simple function of adiabatically conserved, linearly mixing properties of the air; this function is different in saturated than in unsaturated air. In Part I, the new model is used to find analytical solutions for infinitesimal motions in a conditionally unstable, exactly saturated atmosphere. As in previous work, the most unstable circulation is an isolated, cylin-drical, single updraft cloud, surrounded by an infinite expanse of subsiding clear air. In contrast to earlier work, strong downdrafts occur inside the cloud near its edge. In a separate note, it will be shown that all growing circulations of infinitesimal amplitude are station-no “linear” wave-CISK is possible. The most important prediction is that subsidence decays exponentially away from the cloud in a horizontal distance Rs. A simple approximate formula for Rs in terms of the growth rate, viscosity, and Coriolis parameter is derived and rationalized. The prediction of infinite cloud spacing will be resolved by a theory of finite-amplitude convection developed analytically in Part II and numerically in Part III, which predicts a finite minimum cloud spacing related to Rs and the strength of convection.

Conjugate forced convection-conduction plate fin in power law fluids

The heat transfer characteristics of laminar, forced convection flow for power law fluids from a vertical plate fin are studied analytically based on the conjugate convection and conduction theory. The resulting boundary layer equations of fluids are coupled with the one-dimensional heat conduction equation of fin through interfacial conditions. Numerical results for the local heat flux, local heat transfer coefficient, and temperature distribution along the fin surface and overall heat transfer rate under the effects of the conjugate convection-conduction parameter, generalized Prandtl number and fluid flow index are illustrated. The results obtained of the non-Newtonian power law fluid are found to have trends similar to those of the Newtonian fluids.

Validity Tests of the Mixing-Length Theory of Deep Convection

The construction of solar or stellar models is hindered by the difficulty of computing, with sufficient accuracy, the convective fluxes in unstable regions. Although the mixing-length theory of convection has been used for more than three decades, its validity has neither been tested by experiment nor verified by computation. This report presents the results of a three-dimensional numerical simulation of deep and efficient convection that support two conclusions: (i) the basic picture proposed by the mixing-length theory is physically valid-the vertical correlation of the motion of fluid elements is proportional to the pressure scale height; and (ii) some dynamical variables, including the convective flux, can be approximately computed from the structure of the stratification with mixing-length approximations.

Asymptotic theory of convection in a rotating, cylindrical annulus

The problem of convection in a rotating cylindrical annulus heated from the outside and cooled from the inside is considered in the limit of high rotation rates. The constraint of rotation enforces the two-dimensional character of the motion when the angle of inclination of the axisymmetric end surfaces with respect to the equatorial plane is small. Even when the angle of inclination is large only the dependences on the radial and the azimuthal coordinates need to be considered. The dependence on time at the onset of convection is similar to that of Rossby waves. But at higher Rayleigh numbers a transition to vacillating solutions occurs. In the limit of high rotation rates simple equations can be derived which permit the reproduction and extension of previous numerical results.

Erratum: A further uncertainty in the mixing length theory of convection in the structure of late-type stars

The paper ‘A further uncertainty in the mixing length theory of convection in the structure of late-type stars’ by R. J. Tayler was published in Mon. Not. R. astr. Soc. (1986) 220, 793–797. Equation (2.4) should read: $\nabla^\prime_\text {ad}=\nabla_\text {ad}+\lambda_1(B^2/\mu_0P)$.

Properties of r-modes in the Sun

Global oscillations of the Sun (r-modes) with very long periods ∼ 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l ≤ 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. ‘Radial fine splitting’ which lifts the degeneracy in n is very small (20 nHz or less) for all n ≤ 14 trapped in the envelope. But, if splitting could be detected, we would have a valuable new constraint on solar convection theories.

Implications of the VEGA Balloon Results for Venus Atmospheric Dynamics

Both VEGA balloons encountered vertical winds with typical velocities of 1 to 2 meters per second. These values are consistent with those estimated from mixing length theory of thermal convection. However, small-scale temperature fluctuations for each balloon were sometimes larger than predicted. The approximate 6.5-kelvin difference in temperature consistently seen between VEGA-1 and VEGA-2 is probably due to synoptic or planetary-scale nonaxisymmetric disturbances that propagate westward with respect to the planet. There is also evidence from Doppler data for the existence of solar-fixed nonaxisymmetric motions that may be thermal tides. Surface topography may influence atmospheric motions experienced by the VEGA-2 balloon.

Kinetics of latex particle deposition from flowing suspensions

The kinetics of deposition of spherical latex particles onto smooth surfaces from suspensions undergoing stagnation point flow has been determined experimentally using a direct observation technique. (T. D o ̨ broś and T. G. M. Van de Ven, Colloid Polym. Sci. 261, 694, 1983). The barrierless deposition conditions have been achieved by adding a surfactant (CTAB) which at the concentration of 10 −5 M produced a positive charge on latex particles, whereas the collector surface (glass) remained negatively charged. The influence of particle size, varying between 0.5 and 4 μm, suspension concentration, and flow intensity on the rate of particle transfer has been systematically studied. A characteristic feature of the results obtained is a minimum deposition rate for particle size around 1 μm. The experimental results have been interpreted in terms of the convective mass transfer theory (Z. Adamczyk, T. D o ̨ broś, J. Czarnecki, and T. G. M. Van de Ven, Adv. Colloid Interface Sci. 19, 183, 1983; T. D o ̨ broś, Z. Adamczyk, and J. Czarnecki, J. Colloid Interface Sci. 62, 529, 1977; Z. Adamczyk, and T. G. M. Van de Ven, J. Colloid Interface Sci. 89, 497, 1981) and a quantitative agreement within error bounds has been found for all particle sizes and flow rates investigated. This proves also that the numerical analysis of the flow field near the stagnation point is correct.