On vertical heat convection and diffusion in the South Atlantic

Summary It seems that vertical motions in the oceans are essentially determined by the thermal exchanges, viz. turbulent diffusion and convection. Assuming a geostrophic current, the vertical component is computed from the observations made on the Meteor in the southern part of the Atlantic Ocean. The mean vortical velocities obtained range between 1 and 10 cm per day.These results, and the assumption of a balance of the vertical heat fluxes within an intermediate layer, lead to values of the coefficient of diffusion. According to these values, the coefficient varies inversely to the sqare root of the stability.

---

Über die vertikale Wärmekonvektion und -diffusion im südlichen Atlantischen Ozean

Zusammenfassung Vertikale Bewegungen in den Ozeanen scheinen wesentlich durch Wärmeaustausch bedingt zu sein, und zwar durch turbulente Diffusion und Konvektion. Unter der Annahme einer geostrophischen Strömung wird der vertikale Komponent aus den an Bord der Meteor im südlichen Atlantischen Ozean gemachten Beobachtungen berechnet. Die erzielten mittleren Geschwindigkeiten bewegen sich zwischen 1 und 10 cm per Tag.Diese Ergebnisse und die Annahme eines Gleichgewichts der vertikalen Wärmeströmung innerhalb einer Zwischenschicht ermöglichen es, die Werte des Diffusionskoeffizienten zu ermitteln. Nach diesen Werten schwankt der Koeffizient im umgekehrten Verhältnis zur Quadratwurzel der Stabilität.

---

Sur la convection et la diffusion des flux verticaux thermiques dans la partie Sud de l'Océan Atlantique

Résumé Les mouvements verticaux dans les océans semblent être déterminés surtout par des échanges thermiques, c. a. d. par la diffusion turbulente et la convection. Le courant vertical supposé géostrophique est calculé à l'aide des observations faites par le Meteor» dans la partie Sud de l'océan Atlantique. Les vitesses moyennes obtenues sont comprises entre 1 et 10 cm par jour.Ces résultats et l'hypothèse d'un équilibre des flux thermiques verticaux dans une couche intermédiaire permettent d'obtenir des valeurs du coefficient de diffusion. D'après ces valeurs, le ceofficient varie en raison inverse de la racine carrée de la stabilité.

     

Free convection along a non-uniformly heated vertical plate with a variable transverse magnetic field

Summary In this article, we have solved the problem of natural convection along a vertical plate with variable temperature and a transverse non-uniform magnetic field. It also represents a unified analysis of the works of other including the present author, on natural convection with or without transverse magnetic field, and with uniform or non-uniform plate temperature.The author is indebted to Prof.K. B. Ranger, Department of Mathematics, for his continuous and active interest in my research work. I am also grateful to him for offering me a fellowship from his N.R.C. (Canada) research fund.     

Stability of buoyancy opposed mixed convection in a vertical channel and its dependence on permeability

Non-Darcy mixed convective flow of water due to external pressure gradient and buoyancy opposed forces are considered in a vertical channel filled with porous medium, which can be either isotropic or anisotropic. The linear theory of stability analysis has been used to numerically investigate the dependence of the transition behavior of the fully developed basic flow on the permeability of the medium. Numerical experiments indicate that mainly two main instability modes appear: Rayleigh–Taylor (R–T) and buoyant instability. For Darcy numbers (Da) ?10⁻⁹, R–T instability dominates within the entire Reynolds number (Re) range considered here. It was also found that for the same Re, the fully developed base flow is highly unstable (stable) for porous media with high (low) permeability. Further, it was seen that the disturbance isotherm cells migrate from the channel walls toward the centerline when permeability is reduced. Reducing the permeability by one order of magnitude (corresponding to a decrease of Darcy number from 10⁻⁶ to 10⁻⁷) increases base flow stability approximately 20-fold. For higher Reynolds numbers, buoyant, mixed and shear instability of the basic flow were found when Da was increased from 10⁻⁷ to 10⁻³. However, for cases in which permeability and porosity behaved as suggested by Carman–Kozeny relation (CKR), buoyant stability was the only mode of instability. Critical values of the Rayleigh (Ra) and Darcy (Da) numbers in the R–T mode of instability were related to each other by the hyperbolic function RaDa = −2.465.     

Radioactivité artificielle et ozone,traceurs en météorologie dynamique

Résumé La comparaison des mesures de radioactivité et de concentration de l'ozone en un même lieu, montre que l'approvisionnement, dans les deux cas, se fait par arrivées discontinues; ainsi se trouve confirmée l'hypothèse deG. Lambert d'injections à partir de la basse stratosphère à l'occasion de ruptures momentanées de la barrière de la tropopause, conformément aux calculs deStaley. D'autres exemples montrent comment les données fournies par l'ozone et la radioactivité se complètent pour préciser les grands mouvements de l'atmosphère.

---

Summary We have compared the measurements made at the same location on artificial radioactivity of the air and ozone concentration; the results show that in both cases, these products reach ground level by discrete periods of time and not continously. This is in agreement withG. Lambert's assumption of injections from the lower stratosphere throught the tropopause barrier when this barrier is temporarily opened according toStaley's computations. Other examples show how ozone and radioactivity data give complementary information in the field of movements of the atmosphere.

     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.