Comment on rotating hydraulics

Abstract

Numerical solutions of the axisymmetric flows during the relatively early phase of spin-up from rest of a stratified fluid in a cylinder are presented. Detailed results are given for a cylinder of aspect ratio of O(l) and for a minute Ekman number, showing axisymmetric spin-up for three values of the stratification parameter. As the stratification increases, the meridional circulation is confined to a region closer to the Ekman layers. An axisymmetric shear wave propagates radially inward from the sidewall, but, unlike the strictly vertical front for a homogeneous fluid, the interface which separates rotating from nonrotating fluid is bow-shaped. For a stratified fluid, the axial vorticity distribution is nonuniform both in the vertical and in the radial directions. With increasing stratification, diffusive vorticity production near the sidewall is more pronounced. Axisymmetric flows in the early phase of spin-up of a stratified fluid are controlled by both the inviscid dynamic effect and the viscous diffusion effect. At a location close to the Ekman layers, the inviscid effect outweighs the viscous effect, in much the same way as in a homogeneous fluid. However, at a location close to mid-depth, the viscous diffusion effect, enhanced by substantial flow gradients in that region, is dominant. This points to the necessity of including the direct effect of viscous diffusion in the interior in formulating an analytical model of stratified spin-up problems.     

On the spin-up of a stably stratified,electrically conducting fluid. Part 1: Spin-up controlled by the hartmann layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady Hartmann boundary layer control the fluid interior. It is shown how to obtain the known spin-up times for a homogeneous, nonconducting fluid (τ = E ^-½), a stably stratified, nonconducting fluid (τ = (σS/E, E ^?1) and a homogeneous conducting fluid (τ = α^?1 E ^-½) from the present formulation where τ = v/ωt, E = v/ωL ², σS = vN²/κω² and 2α² = σB²/pω. The problem is solved in the parameter range E?α²?1, α²/E?σS using the Laplace transform and two new spin-up times are obtained. Combined into one expression, they are τ = (1 + δ)α^?1E^-½ where δ = σμv. The spin-up mechanism is investigated and it is found that, in contrast to the homogeneous, conducting case, torsional Alfvén waves may be instrumental in the spin-up of a stratified conducting fluid. The effects of viscous and ohmic diffusion on the torsional Alfvén wave fronts are studied and the following regimes are identified: 0 < δ ?E/α², spin-up by meridional circulation of electric current with no Alfvén waves; E^-½/α ? δ ? 1, spin-up by meridional circulation of electric current with transient Alfvén waves; α/E^½ ? δ ? α²/E, spin-up by meridional circulation of current with weak Alfvén waves; 1 ? δ ? α/E^½, spin-up by strong Alfvén waves; α^½/E ? δ ? α²/E, spin-up by viscous diffusion with transient Alfvén waves; α/E ? δ < ∞, spin-up by viscous diffusion with no Alfvén waves.     

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.     

Smoothed particle hydrodynamics pore-scale simulations of unstable immiscible flow in porous media

We have conducted a series of high-resolution numerical experiments using the Pair-Wise Force Smoothed Particle Hydrodynamics (PF-SPH) multiphase flow model. First, we derived analytical expressions relating parameters in the PF-SPH model to the surface tension and static contact angle. Next, we used the model to study viscous fingering, capillary fingering, and stable displacement of immiscible fluids in porous media for a wide range of capillary numbers and viscosity ratios. We demonstrated that the steady state saturation profiles and the boundaries of viscous fingering, capillary fingering, and stable displacement regions compare favorably with micromodel laboratory experimental results. For a displacing fluid with low viscosity, we observed that the displacement pattern changes from viscous fingering to stable displacement with increasing injection rate. When a high viscosity fluid is injected, transition behavior from capillary fingering to stable displacement occurred as the flow rate was increased. These observations are also in agreement with the results of the micromodel laboratory experiments.     

Spin-up of a two-layer fluid in a rotating cylinder

Abstract

we report the results of experiments on the spin-up of two layers of immiscible fluid with a free upper surface in a rotating cylinder over a wide range of internal Froude numbers. Observations of the evolution of the velocity field by particle tracking indicates that spin-up of the azimuthal velocity in the upper layer take much longer than in a homogeneous fluid. Initially, spin-up occurs at a rate comparable to that of homogeneous fluid but, at high internal Froude number, a second phase follows in which the remaining lative motion decays much more slowly. Quantitative comparison of these measurements to the theory of Pedlosky (1967) shows good agreement.

Visualization of the interface displacement during spin-up detected the presence of transient azimuthal variations in the interface elevation over a wide range of Froude (F), Ekman (E), and Rossby (ε) number. nalysis of the occurrence of the asymmetric variations using the parameter space (Q, F), where Q = E ^1/2/ε, suggested by the baroclinic instability theory and experiments of Hart (1972), showed that the flow was stable for Q > 0.06 with no discernable dependence on F. This result, together with the prediction of Pedlosky's theory that radial gradient of potential vorticity in the two layers have opposite signs, suggests at the baroclinic instability mechanism was responsible for the asymmetries. The location and timing of these instabilities may account for the discrepancies between the observations and the Pedlosky (1967) theory.     

The entrainment of high-viscosity magma into low-viscosity magma in eruption conduits

We report experiments on the flow of two fluids of contrasting viscosity through a pipe in which low-viscosity fluid occupies the center of the pipe. The volume flux of the low-viscosity fluid in the pipe increased during an experiment but did not reach 100% in most cases. The transition from high- to low-viscosity-dominated outflow involved a drop in pressure gradient and an increase in flow rate due to reduced viscous resistance in the pipe. Initially, the central flow was thin and parallel-sided, but as its diameter increased the flow became unstable. A sequence of instabilities was observed during the course of each experiment, both in time and as a function of height in the pipe. In the most commonly observed instability the central flow adopted a helical geometry. The transition from parallel-sided to unstable flow first appeared at the top of the pipe and propagated downwards against the flow. Axisymmetric instabilities originating at the pipe entrance were also observed. All forms of instability exhibited entrainment of viscous fluid into the faster moving central flow. Entrainment was extensive early in the existence of the central flow, but later on the volume flux of lower-viscosity fluid in the central flow rose more rapidly than the rate of entrainment and the proportion of lower-viscosity fluid increased with time. These compositional changes determined the viscosity of the central flow which was found to control its diameter and velocity. In banded pumice deposits, silicic pumice without mafic component is commonly erupted alongside banded pumice blocks. We infer that banded pumice may correspond to the central flow in our experiments, i. e., that viscous magma has been incorporated into less viscous melt, and that pure acid pumice is derived from the outer flow. Changes in eruption style may be caused by variations in pressure gradient and flow rate due to changes in the viscosity of the melt in the conduit. Varied mafic/silicic proportions and degree of mixing in magmatic associations are controlled by the bulk volume erupted, discharge rate, initial temperature difference and aspect ratio of the conduit.     

Taylor columns in horizontally sheared flow

Abstract

Solutions of the steady, inviscid, non-linear equations for the conservation of potential vorticity are presented for linearly sheared geostrophic flow over a right circular cylinder. The indeterminancy introduced by the presence of closed streamline regions is removed by requiring that the steady flow retains above topography a given fraction of that fluid initially present there, assuming the flow to have been started from rest. Those solutions which retain the largest fraction in uniform and negatively sheared streams satisfy the Ingersoll (1969) criterion (that, in the limit of vanishingly small viscosity, closed streamline regions are stagnant) and so are unaffected by Ekman pumping. These flows are set up on the advection time scale. In positively sheared flows the maximum retention solutions do not satisfy the Ingersoll criterion and thus would be slowly spun down on the far longer viscous spin-up time.

For arbitrary isolated topography, both the partial retention and Ingersoll problems are reduced to a one-dimensional non-linear integral equation and the solution of the Ingersoll problem obtained in the limit of strong positive shear. The stagnant region is symmetric about the zero velocity line and extends to infinity in the streamwise direction. Its cross-stream width is proportional to the rotation rate and fractional height occupied by the obstacle and inversely proportional to the strength of the shear, decreasing inversely as the square of distance upstream and downstream.     

Dynamics of a spherical viscoelastic shell: Implications to a criterion for fragmentation/expansion of bubbly magma

This paper investigates dynamics of a spherical bubble surrounded by a viscoelastic fluid. The purpose of the study is to understand the parameters which control expansion and fragmentation of bubbly magma by decompression. In particular, we focus on which occurs first, fragmentation or expansion. Supposing that rupture of the bubble wall occurs in a critical stress condition, we calculate the change of the bubble radius and tensile stress at the bubble wall for various decompression rates. Conditions in which tensile stress is stored in the shell are represented in terms of dimensionless parameters. The results are interpreted as follows: when magma viscosity is larger than a critical value, and the decompression time is shorter than viscous expansion time, tensile stress is stored before expansion; when magma viscosity is smaller than the critical value, tensile stress is not stored, no matter how rapid the decompression. Although it is a generally accepted theory that fragmentation is effected by stress conditions and decompression time, exactly how decompression time (t₁) effects the fragmentation is not yet fully understood. This study demonstrates that the stress condition is controlled by the length of the decompression time not relative to the viscoelastic relaxation time (t₁ / τ), but relative to the viscous expansion time (t₁ / τ^l_rlx). As suggested by recent experimental studies, the decompression time relative to viscoelastic relaxation time (t₁ / τ) is also significant to the fragmentation process itself. It indicates that the decompression time effects the fragmentation not through the stress condition. However more work must be completed to fully understand the particular relationship between the decompression time and relaxation time in terms of its influence on fragmentation.     

Displacement and rectification of planetary fluids

Abstract

Laboratory experiments on the decay (spin-up) of fluid motion on the β-plane are compared with theory. Under weakly dissipative conditions, some particles conserve potential vorticity during the entire decay. We also study the rectified mean flow which is produced by the lateral Reynolds Stress when a low frequency force is applied to the planetary fluid. The possible connection of effects with oceanic phenomena is briefly discussed.     

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.     

核幔耦合对地球自由核章动的激发影响

地球自由核章动（FCN）是地幔与液核相互作用的重要动力学现象,其激发机制涉及地表流体层、地幔和地核等圈层之间的耦合,此前研究多利用地表流体层角动量数据单独研究其对FCN的激发,对核幔耦合的影响考虑不足.本文基于角动量守恒理论分析了核幔耦合对FCN周期及振幅的影响,并结合多个大气及海洋角动量函数时间序列首次估算了核幔耦合在FCN激发过程中的贡献.结果表明核幔耦合对FCN周期产生的固定和时变影响对FCN激发的作用均不可忽视,尤其时变影响可达几十个微角秒,对于进一步解释FCN时变特征非常重要;核幔耦合对FCN振幅的直接影响是地表流体层的激发与实测FCN不相符的主要原因,黏滞、电磁和地形等耗散耦合的存在对地表流体的激发振幅有67%左右的减弱效果.     

Convective instabilities in a variable viscosity fluid cooled from above

Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν₀ + ν₁ exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 10⁷ and Rayleigh numbers of up to 10⁸ are studied.For intermediate viscosity contrasts (around 10³), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth z_r (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 10¹⁵?5 × 10¹⁶ m² s^?1 for viscosity in the thermal boundary layer below the plate.     

Inertial waves in a fluid partially filling a cylindrical cavity during spin-up from rest

Abstract

Inertial waves are excited in a fluid contained in a slightly tilted rotating cylindrical cavity while the fluid is spinning up from rest. The surface of the fluid is free. Since the perturbation frequency is equal to the rotation speed resonance occurs at a critical height to radius aspect ratio of the fluid. Detailed study of a particular inertial wave shows that in solid body rotation this “eigenratio” agrees with predictions from linear inviscid theory to within 0.5%. Measured time dependence of the eigenratio during spin-up from rest is a function of the tilt amplitude and agrees favorably with predictions from a numerical study. Mean flow associated with the inertial wave becomes unstable during spin-up and in the steady state. A boundary for the unstable region is found experimentally.     

Low-frequency dilatational wave propagation through fully-saturated poroelastic media

The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems.     

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.     

Analytical models for bubble growth during decompression of high viscosity magmas

Analytical models for decompressional bubble growth in a viscous magma are developed to establish the influence of high magma viscosity on vesiculation and to assess the time-scales on which bubbles respond to decompression. Instantaneous decompression of individual bubbles, analogous to a sudden release of pressure (e.g. sector collapse), is considered for two end-member cases. The infinite melt model considers the growth of an isolated bubble before significant bubble interaction occurs. The shell model considers the growth of a bubble surrounded by a thin shell and is analogous to bubble growth in a highly vesicular magmatic foam. Results from the shell model show that magmas less viscous than 10⁹ Pa s can freely expand without developing strong overpressures. The timescales for pressure re-equilibration are shortened by increased ratios of bubble radius to shell thickness and by larger decompression. Time-scales for isolated bubbles in rhyolitic melts (infinite melt model) are significantly longer, implying that such bubbles could experience internal pressures greater than the ambient pressure for at least a few hours following a sudden release of pressure. The shell model is developed to assess bubble growth during the linear decompression of a magma body of constant viscosity. For the range of decompression rates and viscosities associated with actual volcanic eruptions, bubble growth continues at approximately the equilibrium rate, with no attendant excess of internal pressure. The results imply that viscosity does not have any significant role in preventing the explosive expansion of high viscosity foams. However, for viscosities of >10⁹ Pa s there is the potential for a viscosity quench under the extreme decompression rates of an explosive eruption. It is proposed that the typical vesicularities of pumice of 0.7–0.8 are a consequence of the viscosity of the degassing magmas becoming sufficiently high to inhibit bubble expansion over the characteristic time-scale of eruption. For fully degassed silicic lavas with viscosities in the range 10¹⁰ to 10¹² Pa s time-scales for decompression of isolated bubbles can be hours to many months.     

Viscous entrainment by sinking plumes

Geochemical models invoking several distinct reservoirs in the mantle, with different time histories, raise important questions about the exchange of mass between them. If two of these reservoirs are the upper and lower mantle, above and below about 700 km, then sinking of cold slabs through this level is one of a number of possible ways in which mixing can occur. In addition, if slabs do penetrate the transition zone, surrounding upper layer material will be dragged downwards. We have examined the interaction of very viscous plumes, or slabs, with density and viscosity interfaces in a series of laboratory experiments using fluids of different viscosities and densities and have documented several mechanisms which can lead to significant entrainment and mixing. If a slab remains planar as it passes through a density interface, a boundary layer of lighter fluid is pulled into the lower layer and we predict the consequent mass flux. When a near-vertical slab becomes unstable to folding (as it does if it has a sufficient viscosity contrast with its surroundings and its length is greater than about five times its thickness), there is another more efficient entrainment mechanism: upper layer fluid is trapped between the folds in the slab. The effective entrainment increases as the density difference between the upper and lower layers decreases. An increase in viscosity with depth also leads to buckling instability and folding of the surrounding material into the slab material. On the other hand, when there is substantial density difference between the layers a dense slab can cease to sink through the interface but spread out along the interface because it is unstable and incorporates enough upper layer fluid between its folds to become neutrally buoyant. The range of slab behaviour occurring in the mantle is not known but we draw attention to the various possibilities and to the implications for mass flux between layers.     

Wind and melt driven circulation in a marginal sea ice edge frontal system: a numerical model

A seasonal ice edge zone is a unique frontal system with an air-ice-sea interface. This paper is a report on the numerical results from a quasi-three dimensional, time dependent, non-linear numerical model of circulation at a continental shelf-seasonal ice edge zone. The purpose of the experiments is to model the hydrography and circulation, including upwelling, baroclinic geostrophic flow, and inertial oscillations, at the ice edge with emphasis on examining the driving forces of wind and melting ice. It is suggested that the non-linear acceleration terms and vertical density diffusion terms are negligible and that the horizontal density diffusion terms are of secondary importance within the time and space scales of the experiments. The vertical eddy viscosity terms are important in a spin-up time scale and for Ekman transport and a bottom Ekman layer. The effects of the horizontal eddy viscosity terms are observable (a long-ice jet is diffused away from the ice edge) by the end (72 h) of the model runs.Model results are compared with available oceanographic and meteorological data for verification. The observed and modeled features of melt water induced water column stability, frontal structure, and ice edge upwelling are briefly discussed relative to observed ice edge primary production. Because the model is relatively general in nature, it is readily applicable to other seasonal or marginal ice edge zones in either hemisphere.     

Bubble growth in highly viscous melts: theory, experiments, and autoexplosivity of dome lavas

We examine the physics of growth of water bubbles in highly viscous melts. During the initial stages, diffusive mass transfer of water into the bubble keeps the internal pressure in the bubbles close to the initial pressure at nucleation. Growth is controlled by melt viscosity and supersaturation pressure and radial growth under constant pressure is approximately exponential. At later stages, internal pressure falls, radial growth decelerates and follows the square-root of time. At this stage it is controlled by diffusion. The time of transition between the two stages is controlled by the decompression, melt viscosity and the Peclet number of the system. The model closely fit experimental data of bubble growth in viscous melts with low water content. Close fit is also obtained for new experiments at high supersaturation, high Peclet numbers, and high, variable viscosity. Near surface, degassed, silicic melts are viscous enough, so that viscosity-controlled growth may last for very long times. Using the model, we demonstrate that bubbles which nucleate shortly before fragmentation cannot grow fast enough to be important during fragmentation. We suggest that tiny bubbles observed in melt pockets between large bubbles in pumice represent a second nucleation event shortly before or after fragmentation. The presence of such bubbles is an indicator of the conditions at fragmentation. The water content of lavas extruded at lava domes is a key factor in their evolution. Melts of low water content (<0.2 wt%) are too viscid and bubbles nucleated in them will not grow to an appreciable size. Bubbles may grow in melts with 0.4 wt% water. The internal pressure in such bubbles may be preserved for days and the energy stored in the bubbles may be important during the disintegration of dome rocks and the formation of pyroclastic flows.     

Laboratory investigations of viscous effects in replenished magma chambers

Some laboratory experiments are described which investigate the dynamical effects of replenishment of a magma chamber containing high viscosity magma by hotter, denser and much more fluid magma. In the experiments a layer of hot KNO₃ solution is emplaced beneath cold glycerine, which has a viscosity 3000 times greater. Less dense fluid is released immediately and continuously from the interface as a result of crystallization in the lower layer and rises as plumes through the overlying glycerine. Further crystallization occurs in the plumes, and the crystals fall out; but there is little mixing between the two fluids and a layer of depleted KNO₃ solution forms at the top. The experiments demonstrate that interfacial processes begin to dominate where there are large viscosity differences between adjacent fluid layers as would be the case in a rhyolitic magma chamber replenished by basaltic magma.