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Showing papers on "Rayleigh number published in 1992"


Journal ArticleDOI
TL;DR: In this paper, the authors describe experiments on the directional solidification of aqueous ammonium chloride solutions, where the addition of small amounts of a polymerizing agent permits variation of the solution viscosity independently of thermal conditions, phase diagram, and permeability.
Abstract: Fractional crystallization and partial melting involve relative motion of liquid and solid phases and chemical and thermal interactions between them. To elucidate some physical principles of thermosolutal convection in a reactive porous medium, we describe experiments on the directional solidification of aqueous ammonium chloride solutions. The addition of small amounts of a polymerizing agent permits variation of the solution viscosity independently of thermal conditions, the phase diagram, and permeability. Solutions were cooled from below, and crystallization developed at the base of the tank generating at first a field of thin plumes of light residual fluid, released from the boundary layer at the top of the “mush.” The interstitial fluid within the mush also became unstable eventually, the onset of convection occurring when the porous medium Rayleigh number of the mush reached a critical value. This threshold value was found to be 25 at low initial superheat and to decrease with increasing superheat. Local thermodynamic equilibrium between crystals and liquid within the mush coupled the evolution of temperature, composition, and porosity. Convective motions locally caused dissolution and precipitation, and hence fluctuations of porosity developed. Dissolution occurred preferentially in the central parts of upwellings, and the upflow gradually focused, being ultimately channelized into narrow “chimneys” devoid of crystals. All else being equal, the areal density of chimneys was greater the lower the viscosity. Chimney diameter increased with increasing solution viscosity. In the liquid above the growing mush, the convective plumes were very similar to salt fingers. Depending on solution viscosity and temperature gradient, they exhibited a phenomenon of collective instability such that vertical motion was disrupted by wave instabilities. The base plate temperature chosen was above the eutectic, and hence the total amount of crystals at the end of experiments with the same initial composition and the same final temperature was a constant fixed by the phase diagram. The spatial distribution of crystals and the final porosity of the mush were, however, determined by the strength of compositional convection as measured by the porous medium Rayleigh number. When no convection occurred, mush thickness finally became equal to the initial layer thickness, and the system was homogeneous. When compositional convection occurred, the overlying reservoir underwent chemical evolution, and mush growth slowed dramatically. In experiments with progressively lower solution viscosity (and hence more vigorous convection), final mush thickness was progressively less and final porosity lower. Final mush thickness was found to scale with solution viscosity to the power +0.33. During fractional crystallization of magma the effects of compositional convection can be recorded in the chemical and mineralogical features of cumulate rocks. We speculate that fossil chimney structures can be found in the Lower Zone of the Bushveld ultramafic complex in the form of iron-rich, platinum-bearing dunite pipes. This could explain the adcumulate nature of the Lower Zone rocks and the chemical and mineralogical similarities between the pipes and the overlying Merensky Reef; the Merensky Reef would be interpreted as a hiatus in mush growth. The results may also have applications to the flow structure in regions of partial melting and in the Earth's core.

258 citations


Journal ArticleDOI
Keke Zhang1
TL;DR: In this paper, it was shown that the fundamental features of both thermal instabilities and the corresponding nonlinear convection in rapidly rotating spherical systems (in the range of the Taylor number 109 < T < 1012) are determined by the fluid properties characterized by the size of the Prandtl number.
Abstract: It is shown that the fundamental features of both thermal instabilities and the corresponding nonlinear convection in rapidly rotating spherical systems (in the range of the Taylor number 109 < T < 1012) are determined by the fluid properties characterized by the size of the Prandtl number. Coefficients of the asymptotic power law for the onset of convection at large Taylor number are estimated in the range of the Prandtl number 0.1 ≤ Pr ≤ 100. For fluids of moderately small Prandtl number, a new type of convective instability in the form of prograde spiralling drifting columnar rolls is discovered. The linear columnar rolls extend spirally from near latitude 60° to the equatorial region, and each spans azimuthally approximately five wavelengths with the inclination angle between a spirally elongated roll and the radial direction exceeding 45°. As a consequence, the radial lengthscale of the linear roll becomes comparable with the azimuthal lengthscale. A particularly significant finding is the connection between the new instability and the predominantly axisymmetric convection. Though non-axisymmetric motions are preferred at the onset of convection, the nonlinear convection (at the Rayleigh number of the order of (R—Rc)/Rc = O(0.1)) bifurcating supercritically from the spiralling mode is primarily dominated by the component of the axisymmetric zonal flow, which contains nearly 90% of the total kinetic energy. For fluids of moderately large Prandtl numbers, thermal instabilities at the onset of convection are concentrated in a cylindrical annulus coaxial with the axis of rotation; the position of the convection cylinder is strongly dependent on the size of the Prandtl number. The associated nonlinear convection consists of predominantly non-axisymmetric columnar rolls together with a superimposed weak mean flow that contains less than 10% of the total kinetic energy at (R—Rc)/Rc = O(0.1). A double-layer structure of the temperature field (with respect to the basic state) forms as a result of strong nonlinear interactions between the nonlinear flow and the temperature field. It is also demonstrated that the aspect ratio of the spherical shell does not substantially influence the fundamental properties of convection.

243 citations


Journal ArticleDOI
TL;DR: In this article, the influence of buoyancy force on heat or mass transfer rate was investigated in a stable state thermosolutal convection in a square cavity filled with air, submitted to horizontal temperature and concentration gradient.

229 citations


Journal ArticleDOI
TL;DR: In this paper, the stability of Rayleigh-Be'nard convection in the presence of a plane Couette flow is investigated by numerical computations and it is shown that at Prandtl numbers of the order unity or less these rolls become unstable with respect to the wavy instability which introduces wavy distortions perpendicular to the axis of the rolls.
Abstract: Rayleigh-Be'nard convection in the presence of a plane Couette flow is investigated by numerical computations. From earlier work it is well known that longitudinal rolls are preferred at the onset of convection and that at Prandtl numbers of the order unity or less these rolls become unstable with respect to the wavy instability which introduces wavy distortions perpendicular to the axis of the rolls. In the present analysis the three-dimensional flows arising from these distortions are studied and their stability is considered. A main result is the subcritical existence of three-dimensional flows at Rayleigh numbers far below the critical value for onset of convection.

172 citations


Journal ArticleDOI
TL;DR: In this paper, a study of the convection in acetone due jointly to the thermocapillary (Marangoni) and thermogravitational effects is presented, where the liquid (acetone) is submitted to a horizontal temperature difference.
Abstract: This paper presents a study of the convection in acetone due jointly to the thermocapillary (Marangoni) and thermogravitational effects. The liquid (acetone) is submitted to a horizontal temperature difference. Experiments and numerical simulations both show the existence of three different states : monocellular steady states, multicellular steady states and spatio-temporal structures. The results are discussed and compared with the linear stability analysis of Smith & Davis (1983).

145 citations


Journal ArticleDOI
TL;DR: In this article, a unified approach to derive third-order sets of ordinary differential equations that are asymptotically exact descriptions of weakly nonlinear double convection and that exhibit chaotic behaviour is presented.
Abstract: In certain parameter regimes, it is possible to derive third-order sets of ordinary differential equations that are asymptotically exact descriptions of weakly nonlinear double convection and that exhibit chaotic behaviour. This paper presents a unified approach to deriving such models for two-dimensional convection in a horizontal layer of Boussinesq fluid with lateral constraints. Four situations are considered: thermosolutal convection, convection in an imposed vertical or horizontal magnetic field, and convection in a fluid layer rotating uniformly about a vertical axis. Thermosolutal convection and convection in an imposed horizontal magnetic field are shown here to be governed by the same sets of model equations, which exhibit the period-doubling cascades and chaotic solutions that are associated with the Shil'nikov bifurcation (Proctor & Weiss 1990). This establishes, for the first time, the existence of chaotic solutions of the equations governing two-dimensional magneto-convection. Moreover, in the limit of tall thin rolls, convection in an imposed vertical magnetic field and convection in a rotating fluid layer are both modelled by a new third-order set of ordinary differential equations, which is shown here to have chaotic solutions that are created in a homoclinic explosion, in the same manner as the chaotic solutions of the Lorenz equations. Unlike the Lorenz equations, however, this model provides an accurate description of convection in the parameter regime where the chaotic solutions appear.

116 citations


Journal ArticleDOI
01 Jun 1992-EPL
TL;DR: In this paper, experimental observations of azimuthally traveling waves in rotating Rayleigh-B?nard convection in a circular container are presented and described in terms of the theory of bifurcation with symmetry.
Abstract: Experimental observations of azimuthally traveling waves in rotating Rayleigh-B?nard convection in a circular container are presented and described in terms of the theory of bifurcation with symmetry. The amplitude of the convective states varies as ?? and the traveling-wave frequency depends linearly on ? with a finite value at onset. Here ? = R/Rc - 1, where Rc is the critical Rayleigh number. The onset value of the frequency decreases to zero as the dimensionless rotation rate ? decreases to zero. These experimental observations are consistent with the presence of a Hopf bifurcation from the conduction state expected to arise when rotation breaks the reflection symmetry in vertical planes of the nonrotating apparatus.

113 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of temperature dependent viscosity on the heat transfer rate for a transient free convection flow along a non-isothermal vertical surface is studied employing Karman-Pohlhausen integral method.

113 citations


Journal ArticleDOI
TL;DR: Numerical and analytical models of fluid flow that account for fluid production during prograde regional and contact metamorphism show that expulsion of metamorphic fluids dominates the convective flux when crustal permeabilities are less than 0.1–100 μD, depending primarily on the rate of fluid production.
Abstract: Numerical and analytical models of fluid flow that account for fluid production during prograde regional and contact metamorphism show that expulsion of metamorphic fluids dominates the convective flux when crustal permeabilities are less than 0.1–100 μD, depending primarily on the rate of fluid production. When this is the case, fluid circulation is limited or prevented, fluid pressures are elevated above hydrostatic values, and flow throughout most of the model is up and away from the region of maximum fluid production. Fluid circulation is predicted to occur where permeability is high, in dry rocks, or after rates of fluid production decrease as peak temperatures are reached. Large changes in the pattern of flow and influx of externally derived fluids may thus occur in metamorphic terranes when dehydration wanes or ceases and cooling begins. Inclusion of an impermeable horizon in the models further inhibits fluid circulation. Earlier, shallow hydrothermal models and interpretations based on the Rayleigh number may be inappropriate for characterizing fluid flow during prograde metamorphism at depth because they do not account for fluid production.

97 citations


Journal ArticleDOI
TL;DR: In this paper, the zero-Prandtl-number limit of the Oberbeck-Boussinesq equations is compared to the small Prandtl number Rayleigh-Benard convection through numerical simulations, and a rich variety of regimes are observed as the Rayleigh number is increased.
Abstract: The zero-Prandtl-number limit of the Oberbeck-Boussinesq equations is compared to small-Prandtl-number Rayleigh-Benard convection through numerical simulations. Both no-slip and free-slip boundary conditions, imposed at the top and bottom of a small-aspect-ratio, horizontally periodic box are considered. A rich variety of regimes is observed as the Rayleigh number is increased: supercritical oscillatory instabilities for various values of the aspect ratios, competition between two-dimensional rolls, squares and hexagonal patterns, competition between travelling and standing waves, transition to chaos, and scalings laws for the first Rayleigh-number decade

97 citations


Journal ArticleDOI
TL;DR: In this paper, an extended Boussinesq model of mantle convection with multiple phase transitions and a triple point near the 670 km discontinuity has been proposed, which facilitates numerical computations of convection.

Journal ArticleDOI
TL;DR: In this article, the authors performed a numerical study of natural convection heat transfer from a uniformly heated horizontal cylinder placed in a large air-filled rectangular enclosure using a spectral element method and found that the mean Nusselt number varies with Rayleigh number, Raa, according to a general correlation of the form Nua = C1(Raa)C2, where C1 and C2 are empirical constants that depend on the chosen scale length.

Journal ArticleDOI
TL;DR: In this paper, the effects of compressibility on threedimensional thermal convection in a basally heated, highly viscous fluid spherical shell with an inner to outer radius ratio of approximately 0.55 were investigated.
Abstract: A numerical investigation is made of the effects of compressibility on threedimensional thermal convection in a basally heated, highly viscous fluid spherical shell with an inner to outer radius ratio of approximately 0.55, characteristic of the Earth’s whole mantle. Compressibility is implemented with the anelastic approximation and a hydrostatic adiabatic reference state whose bulk modulus is a linear function of pressure. The compressibilities studied range from Boussinesq cases to compressibilities typical of the Earth’s whole mantle. Compressibility has little effect on the spatial structure of steady convection when the superadiabatic temperature drop across the shell AT,, is comparable to a characteristic adiabatic temperature. When AT,& is approximately an order of magnitude smaller than the adiabatic temperature, compressibility is significant. For all the non-Boussinesq cases, the regular polyhedral convective patterns that exist at large AZ, break down at small AT, into highly irregular patterns ; as AZ, decreases convection becomes penetrative in the upper portion of the shell and is strongly time dependent at Rayleigh numbers only ten times the critical Rayleigh number, (Ra),,. Viscous heating in the compressible solutions is concentrated around the upwelling plumes and is greatest near the top and bottom of the shell. Solutions with regular patterns (and large AEJ remain steady up to fairly high Rayleigh numbers (100(Ra),,), while solutions with irregular convective patterns are time dependent at similar Rayleigh numbers. Compressibility affects the pattern evolution of the irregular solutions, producing fewer upwelling plumes with increasing compressibility.

Patent
16 Dec 1992
TL;DR: In this paper, a liquid heat sink is provided that employs natural convection of a liquid coolant (18') to cool a printed circuit board on which are mounted a plurality of heat-generating components.
Abstract: A liquid heat sink is provided that employs natural convection of a liquid coolant (18') to cool a printed circuit board (14) on which are mounted a plurality of heat-generating components (12). In particular, the spacing d between the heat-generating components and a cold plate (20) used to cool the liquid must be such as to provide a Rayleigh number of at least about 1700 in the Rayleigh equation: ##EQU1## In the above equation, g is the acceleration of gravity, β is the volumetric coefficient of expansion of the liquid coolant, T1 is the temperature of the cold plate, T2 is the temperature of the component to be cooled, ν is the kinematic viscosity of the liquid coolant, and α is the thermal diffusivity of the liquid coolant. The novel heat sink of the present invention allows complete immersion of the component in the liquid to provide maximum heat transfer, while at the same time providing a mounting/packaging scheme that allows full utilization of the desired heat transfer properties.

Journal ArticleDOI
TL;DR: In this article, a finite difference procedure was proposed to solve the cavity aspect ratio and the dimensionless length of the heat source with respect to the vertical symmetry line of the cavity (e = -0.6 to 0.7), the Prandtl number and the Rayleigh number.
Abstract: Natural convection in an enclosed cavity with localized heating from below has been investigated by a finite difference procedure. The upper surface is cooled at a constant temperature and a portion of the bottom surface is isothermally heated while the rest of the bottom surface and the vertical walls are adiabatic. Parameters of the problem are the cavity aspect ratio (A = 1 and 2), dimensionless length (B = 0.06 to 1.0) and position of the heat source with respect to the vertical symmetry line of the cavity (e = -0.6 to 0.7), the Prandtl number and the Rayleigh number (Ra = 0 to 5 x 10 6). The effects of the thermophysical and geometrical parameters on the fluid flow and temperature fields have been studied. The existence of multiple steady-state solutions and the oscillatory behavior for a given set of the governing parameters are demonstrated. Nomenclature A = aspect ratio, L'lH' B = dimensionless length of heat source, t'/L' g = acceleration due to gravity, m/s2 H' = cavity height, m h = local heat transfer coefficient, W/m2-K h = average heat transfer coefficient, W/m2-K k = thermal conductivity of fluid, W/m-K L' = cavity width, m €' = length of heat source, m m, n = wave numbers of initial disturbance, Eq. (15) Nu = Nusselt number based on cavity height, hH'/K Pr = Prandtl number,'via p'_ = pressure, Pa

Book ChapterDOI
01 Jan 1992
TL;DR: In this paper, the development of mathematical models describing mushy zones is reviewed, with particular attention paid to the transport of mass, heat and species in these reacting, two-phase media.
Abstract: The development of mathematical models describing mushy zones is reviewed. Particular attention is paid to the transport of mass, heat and species in these reacting, two-phase media. Dynamical interactions between solidification in mushy regions and three different types of convection are analyzed: convection due to shrinkage or expansion upon change of phase; and buoyancy driven convection driven either by thermal gradients or by solutal gradients. Directions for future reseach into the dynamics of mushy regions are suggested.

Journal ArticleDOI
TL;DR: In this article, the authors studied the mechanism of spontaneous, abrupt changes in thermohaline circulation in an idealized context, using a two-dimensional Boussinesq fluid in a rectangular container, over 5 decades of Rayleigh number.
Abstract: Long-term variability in the ocean’s thermohaline circulation has attracted considerable attention recently in the context of past and future climate change. Drastic circulation changes are documented in paleoceanographic data and have been simulated by general circulation models of the ocean. The mechanism of spontaneous, abrupt changes in thermohaline circulation is studied here in an idealized context, using a two-dimensional Boussinesq fluid in a rectangular container, over 5 decades of Rayleigh number. When such a fluid is forced with a specified distribution of temperature and salinity at the surface - symmetric about a vertical axis - it attains a stable two-cell circulation, with the same symmetry. On the other hand, replacement of the specified salinity surface condition with an appropriate symmetric salt-flux condition leads to loss of stability of the symmetric circulation and gives rise to a new, asymmetric state. The extent of asymmetry depends on the magnitude of the thermal Rayleigh number, Ra, and on the strength of the salinity flux, y. An approximate stability curve in the y-Ra space, dividing the symmetric from the asymmetric states, is obtained numerically, and the entire range of asymmetric flows, from very slight dominance of one cell to its complete annihilation of the other cell, is explored. The physical mechanism of the pitchfork bifurcation from symmetric to asymmetric states is outlined. The effects of three other parameters of the problem are also discussed, along with implications of our results for glaciation cycles of the geological past and for interdecadal oscillations of the present ocean-atmosphere system.

Journal ArticleDOI
TL;DR: In this paper, the authors used the Navier-Stokes equations for the fluid layers and the extended Darcy equation (including Brinkman and Forchheimer terms) for the porous layer to analyze thermal convection due to heating from below in a porous layer underlying a fluid layer.
Abstract: Thermal convection due to heating from below in a porous layer underlying a fluid layer has been analyzed using the Navier-Stokes equations for the fluid layers and the extended Darcy equation (including Brinkman and Forchheimer terms) for the porous layer. The flow is assumed to be two-dimensional and periodic in the horizontal direction. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios of 0, 0.1, 0.2, 0.5, and 1.0, where this ratio is defined as the ratio of the thickness of the fluid layer to that of the porous layer. For the depth ratio of 0.1, the convection is dominated by the porous layer, similar to the situation at onset, even though the Rayleigh number for the fluid layer is well into the supercritical regime.

Journal ArticleDOI
TL;DR: In this paper, a high-resolution, finite-difference numerical study on natural convection in a square cavity is presented, where the vertical sidewatts of the cavity are differentially heated, and a uniform internal heat generation is also present.
Abstract: A high-resolution, finite-difference numerical study is reported on natural convection in a square cavity. The vertical sidewatts of the cavity are differentially heated, and a uniform internal heat generation is also present. Two principal parameters are considered, the internal Rayleigh number RaI, which represents the strength of the internal heat generation, and the external Rayleigh number Rag, which denotes the effect due to the differential heating of the side walls. The internal Rayleigh number varies in the range 1010 RaI ≤ 107, while the external Rayleigh number is set at RaE = 5 x 107 for most computations. As the relative strength of the internal heat generation increases, the flows near the tap portion of the heated sidewall are directed downward. When the effect of the internal heat generation is dominant, the thermal energy leaves the system for the surroundings over the top portion of the heated wall. Only in the bottom pari of the heated wall is heat transfer directed into the system. The...

Journal ArticleDOI
TL;DR: In this article, a hybrid model for phase change problems is presented, which uses arctangent switching functions to switch on the Darcy flow and variable viscosity terms depending on the local value of the fraction solid.
Abstract: A hybrid model for continuum phase-change problems is presented. The hybrid model accounts for flow in regions of concentrated mush, dilute mush, and single-phase liquid. Scale analysis shows that, in dilute mush, the Blake-Kozeny-Carman relation may lead to inaccuracy in the continuum formulation for certain values of the Rayleigh and Darcy numbers. The hybrid model uses arctangent switching functions to switch on the Darcy flow and variable viscosity terms depending on the local value of the fraction solid. Two-dimensional example calculations suggest that the hybrid model more accurately accounts for transport in the dilute mush region.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Rayleigh-Taylor instability of magnetized plasma is nonlinearly stabilized by the external imposition of transverse velocity shear with zero spatial second derivative.
Abstract: It is shown that the Rayleigh–Taylor instability of magnetized plasma is nonlinearly stabilized by the external imposition of transverse velocity shear with zero spatial second derivative. The critical velocity shear required for stabilization is of order γg(ln Ra)1/2, where γg is the linear growth rate and Ra is the Rayleigh number.

Journal ArticleDOI
TL;DR: In this paper, the effects of the vibration frequency and Rayleigh number on thermal convection in a two-dimensional square enclosure induced simultaneously by gravity and vertical vibration is investigated numerically, and two analytic methods are proposed to predict the frequencies of the quasi-static convection and resonant vibration convection regions, respectively.

Journal ArticleDOI
TL;DR: In this paper, the effects of multiple phase-transitions on the dynamics of the Venusian mantle have been investigated with a two-dimensional finite-element method and a depth-dependent thermal expansivity has been employed in a purely basal heating configuration with an aspect-ratio of four.
Abstract: The effects of multiple phase-transitions on the dynamics of the Venusian mantle have been investigated with a two-dimensional finite-element method. A depth-dependent thermal expansivity has been employed in a purely basal heating configuration with an aspect-ratio of four. The addition of the olivine → spinel transition promotes layered convection more so than models with a single spinel → perovskite phase-change. The shifts in the phase-transition depths and the presence of a conductive lid increase the tendency of the Venusian mantle circulation to flow through the transition zone. The potentially lower Rayleigh number in Venus from lack of volatiles will also enhance whole mantle convection. The style of convection in Venus may have changed from layered convection in the past to whole-mantle convection today. This transition might have been responsible for the major resurfacing event on Venus.

Journal ArticleDOI
01 Mar 1992
TL;DR: In this paper, a two dimensional cavity filled with a uniform heat generating, saturated porous medium has been studied and the results are presented in terms of the isotherms and stream functions, the temperature variation and maximum temperature in the cavity and heat transfer from the vertical walls.
Abstract: Steady natural convection heat transfer in a two dimensional cavity filled with a uniform heat generating, saturated porous medium has been studied. The boundary conditions were: Two isothermal walls at different temperatures, two horizontal adiabatic walls. The aspect ratio was varied from 0.1 to 10 and the Rayleigh number from 100 to 108. The results are presented in terms of the isotherms and stream functions, the temperature variation and maximum temperature in the cavity and heat transfer from the vertical walls. The study indicates that asymmetric vertical boundary conditions with θ h >0 has an important effect on the temperature and flow fields as well as on the heat transfer characteristics of the cavity with highly asymmetric results. Various heat transfer modes are identified dependent on the Rayleigh number and the aspect ratio.

Journal ArticleDOI
TL;DR: In this paper, the effect of lateral variations in heat flux or temperature in the lowermost mantle associated with mantle convection was modelled by a rotating spherical shell with uniform lower boundary temperature and a laterally varying upper surface temperature and the solutions found by numerical calculation, some for a density-stratified fluid.
Abstract: SUMMARY Lateral variations in heat flux or temperature in the lowermost mantle, associated with mantle convection, will drive fluid flow in the liquid core. The effect is modelled by a rotating spherical shell with uniform lower boundary temperature and a laterally varying upper surface temperature and the solutions found by numerical calculation, some for a density-stratified fluid. The problem depends upon two dimensionless numbers, a horizontal Rayleigh number and a stratification parameter. The calculations are restricted to surface temperatures which are symmetric about the equator and steady solutions are found. Induced toroidal flows near the surface are closely linked with the applied temperature profile through the thermal wind equation and Coriolis forces make the convection penetrate into the shell. Stratification acts mainly to suppress radial flow but the surface toroidal flow is relatively unaffected. The results illustrate the powerful influence exerted by the surface temperature but are difficult to apply directly to the earth's core because molecular values of the thermal diffusivity entail a very long time-scale. Assuming a turbulent thermal diffusivity equal to the magnetic diffusivity gives a more realistic time-scale and it is possible to recover, for specific simple imposed temperature profiles, flows similar to those found in the earth's core from inversion of geomagnetic secular change.

Journal ArticleDOI
TL;DR: In this article, a hemispherical fluid shell has been constructed to model convection subject to nearly spherically symmetric distributions of gravity and temperature, and the angular velocity is selected such that the paraboloidal surfaces of equal potential match closely surfaces of constant radius within the fluid shell.
Abstract: Convection driven by thermal buoyancy in the presence of the Coriolis force occurs in planetary atmospheres and interiors. In order to model convection subject to nearly spherically symmetric distributions of gravity and temperature, a hemisphere has been constructed which can be rotated about its axis of symmetry. The angular velocity is selected such that the paraboloidal surfaces of equal potential match closely surfaces of constant radius within the hemispherical fluid shell. While the baroclinicity of the fluid state is still noticeable, quantitative measurements can be obtained which can be compared with the theoretical calculations for the spherically symmetric case. The drift of the convection columns has been measured and a transition from the singly periodic state of convection to a modulated state has been visualized and determined quantitatively.

Journal ArticleDOI
TL;DR: In this article, a variety of evidence suggests that at least some hotspots are formed by quasi-cylindrical mantle plumes upwelling from deep in the mantle, such plumes are modeled in cylindrical, axisymmetric geometry with depth-dependent, Newtonian viscosity.
Abstract: A variety of evidence suggests that at least some hotspots are formed by quasi-cylindrical mantle plumes upwelling from deep in the mantle. Such plumes are modeled in cylindrical, axisymmetric geometry with depth-dependent, Newtonian viscosity. Cylindrical and sheet-like, Cartesian upwellings have significantly different geoid and topography signatures. However, Rayleigh number-Nusselt number systematics in the two geometries are quite similar. The geoid anomaly and topographic uplift over a plume are insensitive to the viscosity of the surface layer, provided that it is at least 1000 times the interior viscosity. Increasing the Rayleigh number or including a low-viscosity asthenosphere decreases the geoid anomaly and the topographic uplift associated with an upwelling plume.

Journal ArticleDOI
TL;DR: In this article, the authors studied the time-dependent regime of three-dimensional anelastic compressible convection with depth-dependent thermal expansivity, viscosity and thermal conductivity.
Abstract: Using a spectral code, we have studied the time-dependent regime of three-dimensional anelastic compressible convection with depth-dependent thermal expansivity, viscosity and thermal conductivity in a wide box of size 5 x 5 x 1. Surface Rayleigh numbers up to 5 x 10 exp 6 have been considered. Very few cylindrical plumes are developed at the bottom but they join up collectively to form strong upwellings, which pulsate chaotically. Major descending flows occur in sheets which form rectangular planform at the top. The thermal and flow fields are dominated by large-scale features. The bottom 20 percent of the convecting layer is found to be superadiabatic.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the problem of strongly time-dependent, two-dimensional, incompressible, infinite Prandtl number thermal convection in an aspect-ratio five box for a non-Newtonian power-law rheology and a heated from below configuration, as applied to mantle dynamics.
Abstract: We have studied the problem of strongly time-dependent, two-dimensional, incompressible, infinite Prandtl number thermal convection in an aspect-ratio five box for a non-Newtonian power-law rheology and a heated from below configuration, as applied to mantle dynamics. The convection equations are solved by means of a characteristics-based method with a Lagrangian formulation of the total derivative in the energy equation. Iterations are required at each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly time-dependent to the strongly chaotic or turbulent regime, in which the plumes become disconnected, occurs at much lower Nusselt numbers (Nu), between 20 and 25, than for Newtonian rheology. TheNu versus Rayleigh number(Ra) relationship displays a kink at this transition. Rising non-Newtonian plumes exhibit much greater curvature in their ascent than Newtonian ones and are strongly attracted by descending curr...

Journal ArticleDOI
TL;DR: In this paper, a Chebyshev collocation algorithm is developed to integrate the time-dependent Navier-Stokes equations for natural convection flow with large temperature differences.