Edge-driven convection

We consider a series of simple calculations with a step-function change in thickness of the lithosphere and imposed, far-field boundary conditions to illustrate the influence of the lithosphere on mantle flow. We consider the effect of aspect ratio and far-field boundary conditions on the small-scale flow driven by a discontinuity in the thickness of the lithosphere. In an isothermal mantle, with no other outside influences, the basic small-scale flow aligns with the lithosphere such that there is a downwelling at the lithospheric discontinuity (edge-driven flow); however, the pattern of the small-scale flow is strongly dependent on the large-scale thermal structure of a much broader area of the upper mantle. Long-wavelength temperature anomalies in the upper mantle can overwhelm edge-driven flow on a short timescale; however, convective motions work to homogenize these anomalies on the order of 100 million years while cratonic roots can remain stable for longer time periods. A systematic study of the effect of the boundary conditions and aspect ratio of the domain shows that small-scale, and large-scale flows are driven by the lithosphere. Edge-driven flow produces velocities on the order of 20 mm/yr. This is comparable to calculations by others and we can expect an increase in this rate as the mantle viscosity is decreased.     

On convection in atmosphere

Summary In order to throw light on the mechanics of the cellular patterns of clouds observed from satellites we have applied classical methods to a new class of convection problems, namely a system consisting of two superposed layers with different properties heated from below, and have considered specially the case in which fluid may pass from one layer to the other and change its properties as it does so. A means is provided for computing the critical Rayleigh number and cell width to height ratio when the physical properties of the two layers are given.     

High Prandtl number convection

The theory of convection in a layer heated from below is reviewed with particular emphasis on the limit of infinite Prandtl number. The review is restricted to qualitative properties of the problems which do not depend on special conditions. Similarities and differences between convection in a plane layer and in a spherical shell are pointed out and attention is called to the fact that two-dimensional or axisymmetric forms of convection are realized only in a small region of the parameter space.     

Geoid,Pangea and convection

We show that the present geoid has a simple low-order configuration with an axis of symmetry in the equatorial plane. We show further that it is a “tennis-ball” pattern, with an equatorial high belt and a polar low one, which is clearly controlled by the rotation of the Earth. Finally, we show that the outline of Pangea between at least 200 Ma and 125 Ma ago lay along a great circle passing through the paleo-poles of rotation. Thus, it also had an axis of symmetry in the equatorial plane. This hemispheric super-continent configuration ended in Middle Cretaceous time during a major geologic catastrophe which was accompanied by high rates of spreading, hotspot outbreaks and high sea-level stands. We interpret this evidence in terms of separate steady state lower mantle convection, responsible for the present geoid, weakly coupled to the upper mantle one. This weak coupling leads to the hemispheric continent configuration which ends when excessive heating of the upper mantle due to the insulating continental cap leads to continent dispersal. The complete cycle, from one supercontinent to the next, might be of the order of 400 Ma.     

地幔动力学研究进展--地幔对流

分类而且系统地回顾了地幔对流研究的进展情况.发现虽然静态地幔对流模型(没有考虑地球自转或差异旋转效应)在拟合某些地表观测如重力异常、大地水准面异常以及地下应力场时取得了较满意的结果,但是却对于某些全球尺度的地质特征如0°、180°半球的非对称性显得难以适应,因此建议性地提出了今后地幔对流的可能发展方向.     

Three-dimensional convection in spherical shells

Abstract

In this study, the equations of the three-dimensional convective motion of an infinite Prandtl number fluid are solved in spherical geometry, for Rayleigh numbers up to 15 times the critical number. An iterative method is used to find stationary solutions. The spherical parts of the operators are treated using a Galerkin collocation method while the radial and time dependences are expressed using finite difference methods. A systematic search for stationary solutions has led to eight different stream patterns for a low Rayleigh number (1.28 times the critical number). They can be classified as:

I) Axisymmetrical solutions, analogous to rolls in plane geometry.

II) Solutions which have several ascending plumes within a large area of ascending current, and also several descending plumes within an area of descending current. This type of flow is analogous to bimodal circulation in plane geometry.

III) Solutions characterized by isolated ascending (or descending) plumes separated from each other by a closed polyhedral network of descending (or ascending) currents. This type of circulation is called ‘polygonal’ in analogy with hexagonal circulation in plane geometry.

The behaviour of each of the eight solutions has been studied by increasing the Rayleigh number up to 15 times the critical number. A trend towards transitions from type (I) and type (II) solutions to type (III) solutions is observed. It is inferred that only the “polygonal” solutions are stable for a Rayleigh number greater than 15 times the critical number.     

Thermohaline convection in flowing groundwater

Geothermal activity creates destabilising temperature gradients which are significant in some aquifers. Usually, in such aquifers stabilising salinity gradients also exist. The combination of temperature and salinity distribution in the aquifer may induce various types of hydrodynamic instabilities which were identified in a previous article. The present article concerns the effect of anisotropic characteristics of the hydrodynamic dispersion on the growth of instabilities in the aquifer. Three different mechanisms may lead to instability of the flow field: (a) buoyancy forces may induce convection currents; if the difference between the convection velocity of salt, due to the hydraulic gradients, and that of heat is negligible, then this mechanism is generally most effective in planes parallel to the hydraulic velocity of the fluid (velocity due to the hydraulic gradient); (b) the difference between heat and salt effective diffusivities may lead to overstability; this mechanism is most effective in planes perpendicular to the hydraulic velocity; (c) the difference between the convection velocity of salt and that of heat may induce oscillations which are most effective in planes parallel to the hydraulic velocity. The growth of instabilities in an aquifer of unlimited length is different from their growth in an aquifer of limited length. In the latter thermohaline convection develops in planes perpendicular to the hydraulic velocity, whereas in the former it develops in planes forming an angle θ with the hydraulic gradient. The development of convection cells in the flow field is identified by numerical experiments. These experiments identify the convection cell length and the angle formed between the thermohaline convection plane and the hydraulic gradient.     

Solar convection and magnetic fields

Mike Proctor looks at the interplay between convection and magnetism in the Sun's photosphere, using powerful numerical simulations.     

Some aspects of cumulus convection

Various aspects of the cumulus convection problem, such as the creation of shallow cumulus by cellular convection in the surface layer of the atmosphere, the formation of cloud rolls along the direction of the mean wind and their amplitude modulation, the development of the individual cumulus and their penetration into the inversion layer and the initiation of the squall line type disturbances, are discussed.     

Time-dependent convection at high latitudes

A fully time-dependent ionospheric convection model, in which electric potentials are derived by an analytic solution of Laplaces equation, is described. This model has been developed to replace the empirically derived average convection patterns currently used routinely in the Sheffield/SEL/UCL coupled thermosphere/ionosphere/plasmasphere model (CTIP) for modelling disturbed periods. Illustrative studies of such periods indicate that, for the electric field pulsation periods imposed, long-term averages of parameters such as Joule heating and plasma density have significantly different values in a time-dependent model compared to those derived under the same mean conditions in a steady-state model. These differences are indicative of the highly non-linear nature of the processes involved.     

Intermittent surging movements of a coastal landslide

Since the late 1960s there has been a large mudslide in coastal cliffs of Permo-Triassic strata (conglomerate overlying mudstone) at West Down Beacon, 2 km west of Budleigh Salterton, Devon. A total displacement of 100 m was achieved between 1981 and 1985 as the lobate toe of the mudslide pushed forward across the beach in eleven surges of movement. Each surge involved a displacement of between 5 and 15 m and was completed within a few hours. The toe moved by planar sliding, possibly on more than one seaward-dipping shear surface or zone. Occasionally there were additional relatively minor displacements (less than 1 m), but normally the mudslide was stationary between the major surges. After each surge high-oblique aerial photographs were obtained for stereoscopic interpretation. Debris falls from the cliff appear to have triggered some of the mudslide surges. A displacement recording of one surge has indicated that the rate of movement of the mudslide may have been partly controlled by variations in sea level during the tidal cycle.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

Prevention of Wellbore Clogging by Intermittent Abstraction

Wellfield “Tull en ’t Waal” (water utility Vitens Midden Nederland) suffers extensively from wellbore (or mechanical) clogging. To prevent this type of clogging, wells have been operated intermittently since August 2005 using a carrousel well operation schedule. Since the introduction of this schedule, wellbore clogging has become minimal.     

Transfert vertical d'aerosols par convection artificielle

Pure and Applied Geophysics - Cette brève communication est simplement destinée à faire connaître le début d'expériences de convection artificielle en...     

Penetrative convection in the planetary mantle

Abstract

The hydrodynamic equations for thermal convection in a plane layer of viscous, heat conducting fluid are scaled using the normalization of Ostrach (1965) in which the magnitude of the non-dimensional group τ = gαd/c_p determines the importance of compression work and viscous dissipation in the energy balance of the flow. A linear asymptotic theory valid in the limit τ → ∞ is constructed for the Bénard problem and this is shown to be analogous to Couette flow between contra-rotating cylinders. For sufficiently large τ the flow becomes penetrative. This fact is illustrated for homogeneous fluids by the numerical integration of a set of coupled 1st order differential equations, both for the Bénard and internally heated configurations. The effect of viscosity and thermal conductivity in-homogeneity on the depth of penetration of the main cell in the circulation pattern are assessed and it is concluded that such interactions may be sufficient to effectively limit the depth extent of mantle convection. Finally a discussion of the effect of phase transitions is given following the technique of Busse and Schubert (1971).     

Numerical studies of non-Newtonian mantle convection

Numerical model computations have been carried out to determine how the stress-dependence of non-Newtonian viscosity affects the flow structure of thermal convection. The viscosity laws have been chosen in accordance with present knowledge of upper mantle rheology, based on the diffusion and dislocation creep laws of olivine. The results show that there are important differences between the structures of Newtonian and non-Newtonian convection. While the Newtonian models are insufficient in some respects, the non-Newtonian solutions can explain the characteristics of the real mantle flow. However, this may require a faster plastic deformation than power law dislocation creep, at least in the high-stress regions of the mantle, e.g. at the active plate margins.     

Core cooling by subsolidus mantle convection

Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.