On the interaction between convection and crystallization in cooling magma chambers

We investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers. Because nucleation requires a finite amount of undercooling, crystallization is not instantaneous. For typical values of the rates of nucleation and crystal growth, the characteristic time-scale of crystallization is about 10³–10⁴ s. Roof convection is characterized by the quasi-periodic formation and instability of a cold boundary layer. Its characteristic time-scale depends on viscosity and ranges from about 10² s for basaltic magmas to about 10⁷ s for granitic magmas. Hence, depending on magma viscosity, convective instability occurs at different stages of crystallization. A single non-dimensional number is defined to characterize the different modes of interaction between convection and crystallization.Using realistic functions for the rates of nucleation and crystal growth, we integrate numerically the heat equation until the onset of convective instability. We determine both temperature and crystal content in the thermal boundary layer. Crystallization leads to a dramatic increase of viscosity which acts to stabilize part of the boundary layer against instability. We compute the effective temperature contrast driving thermal convection and show that it varies as a function of magma viscosity and hence composition.In magmas with viscosities higher than 10⁵ poise, the temperature contrast driving convection is very small, hence thermal convection is weak. In low-viscosity magmas, convective breakdown occurs before the completion of crystallization, and involves partially crystallized magma. The convective regime is thus characterized by descending crystal-bearing plumes, and bottom crystallization proceeds both by in-situ nucleation and deposition from the plumes. We suggest that this is the origin of intermittent layering, a form of rhythmic layering described in the Skaergaard and other complexes. We show that this regime occurs in basic magmas only at temperatures close to the liquidus and never occurs in viscous magmas. This may explain why intermittent layering is observed only in a few specific cases.     

Intermittent convection

Abstract

A theoretical analysis of pseudo two-dimensional, finite-amplitude, thermal convection is made for an infinite Prandtl number fluid which is subjected to a constant heat flux out of the top boundary and insulated at the bottom. For large Rayleigh numbers the convective flow becomes intermittent and the system is characterized by the following cyclic process: the formation of a thermal boundary layer by diffusion, the instability of this layer when it becomes sufficiently thick, the destruction of the layer by the convective flow, the dying down of the convection, and the reforming of the thermal boundary layer by diffusion. The periodicity and the horizontal wave number of the intermittent convective flow are found to be independent of the depth of the fluid layer but depend on the rate of cooling and the properties of the fluid.     

Properties of low‐frequency trapped mode in viscous‐fluid waveguides

We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10^?3 Hz to 10³ Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.     

The effect of a shallow low viscosity zone on the apparent compensation of mid-plate swells

A simple model for mid-plate swells is that of convection in a fluid which has a low viscosity layer lying between a rigid bed and a constant viscosity region. Finite element calculations have been used to determine the effects of the viscosity contrast, the layer thickness and the Rayleigh number on the flow and on the perceived compensation mechanism for the resulting topographic swell. As the viscosity decreases in the low viscosity zone, the effective local Rayleigh number for the top boundary layer of the convecting cell increases. Also, because the lower viscosity facilitates greater velocities in the low viscosity zone, the low viscosity layer produces proportionally greater horizontal flow near the conducting lid, causing the base of the conducting lid to appear like a free boundary. The change in the local Rayleigh number and in the effective boundary condition both cause the top boundary layer to thin. Through a Green's function analysis, we have found that the low viscosity zone damps the response of the surface topography to the temperature anomalies at depth, whereas it causes the gravity and geoid response functions to change sign at depth counteracting the positive contributions from the shallower temperature variations. By increasing the viscosity contrast, the conbined effects of the thinning of the boundary layer and the behaviour of the response functions allow the apparent depth of compensation to become arbitrarily small. Therefore, shallow depths of compensation cannot be used to argue against dynamic support of mid-plate swells. Furthermore, we compared the distribution of the effective compensating densities, which is used to obtain the geoid, to that of Pratt compensation, which is often used to calculate the depth of compensation from geoid and topography data for mid-plate swells. For all of our calculations including those with no low viscosity layer, the effective gravitational mass distribution is more complex than assumed in simple Pratt models, so that the Pratt models are not an appropriate gauge of the compensation mechanism.     

Lithospheric necking: a dynamic model for rift morphology

Rifting is examined in terms of the growth of a necking instability in a lithosphere consisting of a strong plastic or viscous surface layer of uniform strength overlying a weaker viscous substrate in which strength is either uniform or decreases exponentially with depth. As the lithosphere extends, deformation localizes about a small imposed initial perturbation in the strong layer thickness. For a narrow perturbation, the resulting surface topography consists of a central depression and uplifted flanks; the layer thins beneath the central depression. The width of the rift zone is related to the dominant wavelength of the necking instability, which in turn is controlled by the layer thickness and the mechanical properties of the lithosphere. For an initial thickness perturbation with a width less than the dominant wavelength, deformation concentrates into a zone comparable to the dominant wavelength. If the initial perturbation is wider than the dominant wavelength, then the width of the zone of deformation is controlled by the width of the initial perturbation; deformation concentrates in the region of enhanced thinning and develops periodically at the dominant wavelength. A surface layer with limiting plastic (stress exponent n = ∞) behavior produces a rift-like structure with a width typical of continental rifts for a strong layer thickness consistent with various estimates of the maximum depth of brittle deformation in the continental lithosphere. The width of the rift is essentially independent of the layer/substrate strength ratio. For a power law viscous surface layer (n = 3), the dominant wavelength varies with layer/substrate strength ratio to the one-third power and is always larger than for a plastic surface layer of the same thickness. The great widths of rift zones on Venus may be explained by unstable extension of a strong viscous surface layer.     

Hot springs mediate spatial exchange of heat and mass in the enclosed sediment domain: A stability perspective

In many natural environments, such as in underwater hot springs and hydrothermal vents, thermal gradients are accompanied with changes in the concentration of chemical compounds transported to the seawater, causing the so-called double-diffusive, mixed convection. To study the physical scenarios in such systems, a vertical channel filled with a porous medium saturated with saline water is considered. The motion in the sediment-filled channel is induced by two buoyancy forces and an external pressure gradient, similar to the situation in a vent with an upward flow direction. The fluid flow has been modeled by an extended Darcy model, and the flow instability mechanisms have been studied numerically. The linear stability analysis is performed considering a wide range of Darcy number (Da = 10⁻⁵ -10⁻⁸). The instability boundary curve showed three distinct dynamic regimes: (i) Rayleigh-Taylor (R-T), (ii) log-log non-linear variation, and (iii) log-log linear variation. The domain of different regimes were sensitive to external pressure gradient as well as permeability. Similar to cross-diffusive natural convection in pure viscous fluids, a linear relationship between logarithmic absolute values of critical thermal Rayleigh number (∣Ra_T∣) and solute Rayleigh number (Ra_C) is found in the third regime. Based on the permeability, for any solute Rayleigh number (Ra_C), there existed a minimum value of Reynolds number (Re), below which R-T type of instability appeared. Above this minimum value, the instability was due to two buoyancy forces, known as buoyant instability. Simulations of secondary flow via energy analysis demonstrated the development of complex dynamics at the critical state in all three regimes characterized by transition of multi to uni-cellular structures and vice verse.     

Prerequisites for density-driven instabilities and convective mixing under broad geological CO2 storage conditions

Direct atmospheric greenhouse gas emissions can be greatly reduced by CO₂ sequestration in deep saline aquifers. One of the most secure and important mechanisms of CO₂ trapping over large time scales is solubility trapping. In addition, the CO₂ dissolution rate is greatly enhanced if density-driven convective mixing occurs. We present a systematic analysis of the prerequisites for density-driven instability and convective mixing over the broad temperature, pressure, salinity and permeability conditions that are found in geological CO₂ storage. The onset of instability (Rayleigh–Darcy number, Ra), the onset time of instability and the steady convective flux are comprehensively calculated using a newly developed analysis tool that accounts for the thermodynamic and salinity dependence on solutally and thermally induced density change, viscosity, molecular and thermal diffusivity. Additionally, the relative influences of field characteristics are analysed through local and global sensitivity analyses. The results help to elucidate the trends of the Ra, onset time of instability and steady convective flux under field conditions. The impacts of storage depth and basin type (geothermal gradient) are also explored and the conditions that favour or hinder enhanced solubility trapping are identified. Contrary to previous studies, we conclude that the geothermal gradient has a non-negligible effect on density-driven instability and convective mixing when considering both direct and indirect thermal effects because cold basin conditions, for instance, render higher Ra compared to warm basin conditions. We also show that the largest Ra is obtained for conditions that correspond to relatively shallow depths, measuring approximately 800 m, indicating that CO₂ storage at such depths favours the onset of density-driven instability and reduces onset times. However, shallow depths do not necessarily provide conditions that generate the largest steady convective fluxes; the salinity determines the storage depth at which the largest steady convective fluxes occur. Furthermore, we present a straight-forward and efficient procedure to estimate site-specific solutal Ra that accounts for thermodynamic and salinity dependence.     

Large aspect ratio cells in two-dimensional thermal convection

Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 10⁵ and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated.     

Heat transport by variable viscosity convection and implications for the Earth's thermal evolution

The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers (Ra) is 10⁴?10⁷ and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number (Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ?ln(Nu)/? ln(Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history.     

Convection in a variable-viscosity fluid: Newtonian versus power-law rheology

A number of finite-element calculations of convection in a variable-viscosity fluid have been carried out to investigate the effects of non-Newtonian flow when rheology is also subject to a strong temperature and pressure influence. A variety of cases has been studied in the range of effective Rayleigh numbers between 10⁴ and 10⁶, including different modes of heating and a range of values for activation energy and activation volume. Power-law creep with a stress exponent of 3 turns out to lead to considerably different flow pattern and heat transfer properties than Newtonian rheology. In general, the effect is to reduce viscosity contrasts imposed by p,T dependence, which can lead in some circumstances to the mobilisation of otherwise stagnant regions within the cell. The properties of non-Newtonian flow can be closely imitated by a Newtonian fluid with a reduced value of the activation enthalpy bH^* with b?0.3–0.5. It appears possible that non-Newtonian rheology plays a key role in determining the convective style in a planetary mantle.     

A simple model of convection in the terrestrial planets

Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.     

On the transition between axisymmetric and non-axisymmetric flow in a rotating liquid annulus subject to a horizontal temperature gradient: Hysteresis effects at moderate Taylor number and baroclinic waves beyond the eady cut-off at high Taylor number

Abstract

The transition between axisymmetric and non-axisymmetric régimes of flow in a rotating annulus of liquid subject to horizontal temperature gradient is known from previous experimental studies to depend largely on two dimensionless parameters. These are Θ, which is proportional to the impressed density contrast Δρ and inversely proportional to the square of the angular speed of rotation ω, and  (Taylor number), which is proportional to ω² /v² where v is the coefficient of kinematic viscosity. At moderate values of , around 10⁷, the critical value of Θ above which axisymmetric flow is found to OCCUT and below which non-axisymmetric fully-developed baroclinic waves (sloping convection) occur, is fairly insensitive to . Though sharp, the transition exhibits marked hysteresis when the upper surface of the liquid is free (but not when the upper surface is in contact with a rigid lid), and it is argued on the basis of the experimental evidence supported by various results of baroclinic instability theory that both the sharpness of the transition and the hysteresis phenomenon are consequences of the combined effects of potential vorticity gradients and viscosity on the process of sloping convection.

We also present some new experiments on fully-developed baroclinic waves, conducted in a large rotating annulus using liquids of very low viscosity (di-ethyl ether), thus attaining values of  as high as 10⁹ to 10¹⁰. The transition from axisymmetric to non-axisymmetric flow is found to lose its sharpness at such high values of , and it is argued that this occurs because viscosity is no longer able to inhibit instabilities at wavelengths less than the so-called ‘Eady short-wave cut-off’, which owe their existence to potential vorticity gradients in the main body of the fluid.     

Convection of a fluid with strongly temperature and pressure dependent viscosity

Plate tectonics on the Earth is a surface manifestation of convection within the Earth’s mantle, a subject which is as yet improperly understood, and it has motivated the study of various forms of buoyancy-driven thermal convection. The early success of the high Rayleigh number constant viscosity theory was later tempered by the absence of plate motion when the viscosity is more realistically strongly temperature dependent, and the process of subduction represents a continuing principal conundrum in the application of convection theory to the Earth. A similar problem appears to arise if the equally strong pressure dependence of viscosity is considered, since the classical isothermal core convection theory would then imply a strongly variable viscosity in the convective core, which is inconsistent with results from post-glacial rebound studies. In this paper we address the problem of determining the asymptotic structure of high Rayleigh number convection when the viscosity is strongly temperature and pressure dependent, i.e. thermobaroviscous. By a method akin to lid-stripping, we are able to extend numerical computations to extremely high viscosity contrasts, and we show that the convective cells take the form of narrow, vertically-oriented fingers. We are then able to determine the asymptotic structure of the solution, and it agrees well with the numerical results. Beneath a stagnant lid, there is a vigorous convection in the upper part of the cell, and a more sluggish, higher viscosity flow in the lower part of the cell. We then offer some comments on the possible meaning and interpretation of these results for planetary mantle convection.     

Small-scale convection under the back-arc occurring in the low viscosity wedge

Water released from subducting slabs through a dehydration reaction may lower the viscosity of the mantle significantly. Thus, we may expect a low viscosity wedge (LVW) above the subducting slabs. The LVW coupled with a large-scale flow induced by the subducting slabs may allow the existence of roll-like small-scale convection whose axis is normal to the strike of the plate boundary. Such a roll structure may explain the origin of along-arc variations of mantle temperature proposed recently in northeast Japan. We study this possibility using both 2D and 3D models with/without pressure- and temperature-dependent viscosity. 2D models without pressure and temperature dependence of viscosity show that, with a reasonable geometry of the LVW and subduction speed, small-scale convection is likely to occur when the viscosity of the LVW is less than 10¹⁹ Pa s. Corresponding 3D model studies reveal that the wavelength of rolls depends on the depth of the LVW. The inclusion of temperature-dependent viscosity requires the existence of further low viscosity in the LVW, since temperature dependence suppresses the instability of the cold thermal boundary layer. Pressure (i.e. depth) dependence coupled with temperature dependence of the viscosity promotes short wavelength instabilities. The model, which shows a relatively moderate viscosity decrease in the LVW (most of the LVW viscosity is 10¹⁸∼10¹⁹ Pa s) and a wavelength of roll ∼80 km, has a rather small activation energy and volume (∼130 kJ/mol and ∼4 cm³/mol) of the viscosity. This small activation energy and volume may be possible, if we regard them as an effective viscosity of non-linear rheology.     

Thermal convection in a twisted horizontal magnetic field

The onset of convection in a layer of an electrically conducting fluid heated from below is considered in the case when the layer is permeated by a horizontal magnetic field of strength B ₀ the orientation of which varies sinusoidally with height. The critical value of the Rayleigh number for the onset of convection is derived as a function of the Chandrasekhar number Q. With increasing Q the height of the convection rolls decreases, while their horizontal wavelength slowly increases. Potential applications to the penumbral filaments of sunspots are briefly discussed.     

One-dimensional modelling of mantle flow

A one-dimensional model of flow between a fixed boundary at the bottom and a moving one on top with no net flow through vertical sections is tested for geophysically interesting mantle viscosity-depth functions. Such a model, although simplistic, may help in answering the question to what depth the return flow extends, at least in the case of moving plates measuring many thousand kilometers across, such as the Pacific plate.It the viscosity in the asthenosphere is less than three orders of magnitude smaller than that of the mantle below, the return flow extends to great depth and the asthenosphere is a zone of concentrated shear. If the viscosity contrast is greater, the return flow is concentrated in the asthenosphere. For a wide range of model parameters typical flow velocities below the asthenosphere are about one-tenth of the plate velocity. The pressure gradient required by the mantle flow may be manifest in gravity trends across moving plates, but no excessive gravity anomalies are required by the model if the absolute viscosity values conform to those inferred from post-glacial rebound data. A thinner and lower-viscosity layer is favored over a thicker and more viscous layer if both fit glacial rebound evidence. The present model may not be applicable if down to the core the viscosity is as low as about 10²¹ N s m^–2 with a free-slip bottom boundary.     

Convective Instability of a Mushy Layer - I: Uniform Permeability

Mushy layers arise and are significant in a number of geophysical contexts, including freezing of sea ice, solidification of magma chambers and inner-core solidification. A mushy layer is a region of solid and liquid in phase equilibrium which commonly forms between the liquid and solid regions of a solidifying system composed of two or more constituents. We consider the convective instability of a plane mushy layer which advances steadily upwards as heat is withdrawn at a uniform rate from the bottom of a eutectic binary alloy. The solid which forms is assumed to be composed entirely of the denser constituent, making the residual liquid within the mush compositionally buoyant and thus prone to convective motion. In this article we focus on the large-scale mush mode of instability, arguing that the 'boundary-layer' mode is not amenable to the standard stability analysis, because convective motions occur on that scale for any non-zero value of the Rayleigh number. We quantify the minimum critical Rayleigh number and determine the structure of the convective modes of motion within the mush and the associated deflections of the mush-melt and mush-solid boundaries. This study of convective perturbations differs from previous analyses in two ways; the inhibition of motion and deformation of the mush-melt interface by the stable stratification of the overlying melt is properly quantified and deformation of the mush-solid interface is permitted and quantified. We find that the mush-melt interface is almost unaffected by convection while significant deformation of the mush-solid interface occurs. We show that each of these effects causes significant (unit-order) changes in the predicted critical Rayleigh number. The marginal modes depend on three dimensionless parameters: a scaled eutectic temperature, τ _e (which characterizes the eutectic temperature relative to the depression of the liquidus), a scaled superheat, τ_∞ (which measures the amount by which the temperature of the incoming melt exceeds the liquidus temperature) and the Stefan number, S (which measures the latent heat of crystallization). To survey parameter space, we focus on seven cases, a standard case having S = τ_∞ = τ _e = 1, and six others in which one of the parameters is either large or small compared with unity: a nearly pure case (τ _e = 100; having little of the light constituent), the large superheat limit (τ_∞→ ∞), a case of large latent heat (S = 100), the near eutectic limit (τ _e → 0), a case of small superheat (τ_∞ = 0.01) and the case of zero latent heat (S = 0). The critical Rayleigh number and the associated wavelength of the convection pattern are determined in each case. The eigenvector for each case is presented in terms of the streamlines and the isolines of the perturbation temperature and solid fraction.     

A model of thermal convection in the major planets with a strongly density-stratified atmospheric layer

Abstract

As an extension of a model by Busse (1983a), a two-layer model of thermal convection in the self-gravitating rotating spherical fluid is considered. The upper layer with arbitrary vertical distributions of density and potential temperature representing the atmospheric layer of major planets is imposed on the spherical Boussinesq fluid. The Prandtl number P and the ratio of the mass of the upper layer to that of the lower layer are used as small expansion parameters. The modification of the critical Rayleigh number by imposing the upper layer are clearly separated into two parts, proportional to (1) the mass of the upper layer and to (2) an integral representing a measure of convective instability of the upper layer. Some implications for atmospheric dynamics of the major planets are also presented.     

Analytical modelling of viscous diapirism through a strongly non-Newtonian overburden subject to horizontal forces

We study the early stages of diapirism and analyse the gravitational and buckling instabilities of a buoyant viscous layer overlain by a layer of strongly non-Newtonian power-law rheology (when a power-law exponent tends to infinity). This situation models rocksalt under a layer of a perfectly plastic overburden. The growth rate of small perturbations on the interface between the two layers and the wavelength of the most unstable perturbations are found and compared with those of structures consisting of two Newtonian or two strongly non-Newtonian viscous layers. Effects due to the effective viscosity and thickness ratios between the two layers are assessed. Considering the effective viscosity of the overburden to be much greater than the viscosity of the buoyant salt layer, we obtain the following results. In the case of simple gravitational instability and no-slip boundary conditions, the instability pattern is similar to that in a strongly non-Newtonian power-law material. An increase in the thickness of the overburden decreases the dominant wavelength of the most unstable mode, while the dominant wavelength is lengthened in the case of Newtonian viscous layers. When the system of layers is subjected to either horizontal extension or shortening, and the upper boundary of the system is stress-free, the buckling instability overwhelms the gravitational instability, and the dynamic growth rate of the instability depends linearly on the effective viscosity ratio. We conclude that the introduction of strongly non-Newtonian power-law rheology into diapir overburdens greatly affects instability parameters such as growth rate and dominant wavelength of perturbations and hence, alters interdiapir spacings.     

Planform of convection with strongly temperature-dependent viscosity

Abstract

This paper experimentally investigates the convective planform near critical in a fluid layer whose temperature-dependent viscosity varies from top to bottom by up to a factor of 1500. Convection occurs in three different planforms: rolls, hexagons and squares. The square planform, which appears only for fluids with viscosity variation greater than about 50, replaces the hexagonal convection pattern as the Rayleigh number increases much above critical. The large amplitude of hexagonal convection with strong viscosity variation precludes studying the hexagon-square transition with perturbation methods of the type used to study the hexagon-roll transitions at smaller viscosity variations.