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1.
Summary Stewartson [1]2) has considered the inviscid flow past a sphere in the presence of a uniform magnetic field andMurray andLudford [2] have investigated a similar problem in which the magnetic field originates from an axially symmetric dipole field situated at the centre of the sphere. In connection with the study of earth's magnetic field, the toroidal part of this field plays a dominant part. This gives rise to the importance of studying the effect of a toroidal magnetic field on flows past different bodies of revolution; specially past spheres and spheroids. In the present note inviscid flows past a sphere, and a spheroid, are considered, for the case of a toroidal magnetic field originating in the fluid. In the case of the sphere the field inside the sphere consists of an electric dipole directed along the axis of symmetry together with a uniform electric field which produces a uniform current along the axis. In the case of the spheroid, the field inside it is due to an electric dipole and quadrupole directed along the axis of symmetry, together with a uniform electric field which produces a uniform current along this axis.  相似文献   

2.
Summary Numerical calculations were carried out to determine the effect of a vertical electric field on the efficiency with which electrically charged or uncharged cloud drops and small raindrops of diameters ranging from 84 m to 1.248 mm collide with electrically charged or uncharged particles of density 2 gm/cm3 and diameters between 1 and 20 m. For this purpose, numerical flow fields about spheres of Reynolds numbers ranging from 1 to 400 were used to integrate the trajectory of the particle relative to the drop, and the force between two conducting spheres was used to represent the electrostatic force on the particle. The effect of thunderstorm strength electric charges and field on the collision efficiency was found to be highly significant for the smaller collector drops, and declined to insignificance for the largest collector drop.  相似文献   

3.
Summary Expressions are obtained for the currents induced in a conducting sphere placed in an oscillating uniform field. The induced currents are plane circular loops around the axis of symmetry with respect to the external field. Current profiles are presented at three latitudinal planes inside the sphere for three parametric values of that are of importance in prospecting. Magnetic fields created by these currents loops at a point on the axis of the sphere are calculated. This study reveals some interesting results like the existence of zones contributing positively and negatively to the signal measured outside the sphere and behaviour of these zones with parameter.  相似文献   

4.
Induced stresses due to fluid extraction from axisymmetric reservoirs   总被引：1，自引：0，他引：1  
Earthquakes can be induced by fluid extraction, as well as by fluid injection.Segall (1989) proposed that poroelastic stresses are responsible for inducing earthquakes associated with fluid extraction. Here, I present methods for computing poroelastic stress changes due to fluid extraction for general axisymmetric reservoir geometries. The results ofGeertsma (1973) for a thin disk reservoir with uniform pressure drop are recovered as a special case. Predicted surface subsidence agrees very well with measured leveling changes over the deep Lacq gas field in southwestern France. The induced stresses are finite if the reservoir pressure changes are continuous. Computed stress changes are on the order of several bars, suggesting that the preexisting stress states in regions of extraction induced seismicity are very close to frictional instability prior to production.  相似文献   

5.
Sommario Dopo aver richiamato l'ampliamento ad un campo potenziale spaziale delle formule diLegendre che risolvono il primo problema fondamentale della Geodesia, l'A. applica tali formule al caso del campo diSomigliana, che ammette l'ellissoide come una delle superfici equipotenziali della famiglia; tale applicazione rappresenta la più naturale estensione ad un campo tridimensionale delle classiche formule ellissoidiche superficiali, e si accorda con l'adozione internazionale del campo diSomigliana per tutte le speculazioni della Geodesia dinamica.
Summary After having recalled the extension to a spatial potential field ofLegender's formulae solving the first fundamental problem in Geodesy, the author applies such formulae toSomigliana's field, which admits the ellipsoid as one of the equipotential surfaces of the family. Such application represents the most natural extension to a three-dimensional field of the classical ellipsoidal surface formulae, and agrees with the international adoption ofSomigliana's field in dynamic Geodesy.
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6.
Investigation was carried out to study the interaction of positive streamers with charged and uncharged drops in a vertical electric field configuration. Results obtained for vertical and horizontal positions of the photographic films show that streamer interactions with neutral and negative drops are similar and further confirmed earlier results byPhelps (1972). It showed that indirect streamer interaction with droplets is effected by branches being sent to the drops from the main channel. The visibility of the branches on the Lichtenberg figures and the degree of interaction of streamers with drops depend on the drop size, its initial charge and shape, and/or the separation of the drops from the main channel. Suppression of streamer propagation among the positively charged drops was observed.  相似文献   

7.
Summary Second derivative coefficients for various grid systems are derived followingPeters' andElkins' approaches. Two simple formulae, one for three dimensional bodies and the other for two dimensional bodies are also suggested. These utilise the average of the anomalies around a single circle and the anomaly at the central point.All the coefficient sets and the proposed simple formulae are applied to gravity fields of spheres and cylinders. Coefficients ofElkins' type derived with a weightage of 1/r 4 to all the circles gave excellent results in both the cases of spheres and cylinders, whereasPeters' coefficients without any weightage to the circles gave reliable results in case of cylinders only. The simple formulae suggested gave more accurate results than any of the above coefficient sets.  相似文献   

8.
Summary In the present note, an attempt has been made to investigate the wave-motions in a poro-viscoelastic medium traversed by a static magnetic field, by using the equations ofMaxwell, and those ofBiot.  相似文献   

9.
The time-domain EM response of a conducting sphere has been subject of past studies with a particular goal of understanding the response of steel unexploded ordnance items. A change in formulas and parameter definition between authors has created inconsistency between published results and analytic formulas. Correction of formulas is required for further studies based on the conducting permeable sphere.  相似文献   

10.
Abstract

A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radius r 0, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis. The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere. We are primarily interested in the limit where the ratio q of the thermal diffusivity κ to the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance.

Thermal convection sets in when the temperature gradient exceeds some critical value as measured by the modified Rayleigh number Rc. The critical temperature gradient is smallest (Rc reaches a minimum) when the magnetic field strength parameter Λ ? 1. [Rc and Λ are defined in (2.3).] The instability takes the form of a very slow wave with frequency of order κ/r 2 0 and its direction of propagation changes from eastward to westward as Λ increases through Λ c ? 4.

When the fluid is sufficiently stably stratified and when Λ > Λm ? 22 a new mode of instability sets in. It is magnetically driven but requires some stratification before the energy stored in the magnetic field can be released. The instability takes the form of an eastward propagating wave with azimuthal wavenumber m = 1.  相似文献   

11.
Summary Expressions are obtained for the currents induced inside a conducting sphere placed in the field of an oscillating magnetic dipole. Interesting conclusions can be drawn from an analysis of the formulas for the current induced due to different orientations of the dipole.  相似文献   

12.
Summary The concept of comet orbit activity sphere as introduced byD'Alembert and developed byLaplace is modified and applied to the Sun-Earth-Moon system, leading to a new approximate relationship between astronomical constants usually regarded as independent quantities. When Sun-Earth mass ratio, the astronomic unit, and Earth-Moon separation distance are taken as known, an elementary algebraic formula gives the Earth-Moon mass ratio in terms of these. Despite the inherently imprecise character of this type of calculation, surprisingly close numerical agreement with independently determined values is obtained. The great simplicity and directness of the result contrast with ardous orthodox inference procedures for the lunar mass, suggesting that newer methods of general dynamic analysis are required in the study of asymptotic states of the three-body problem.  相似文献   

13.
Summary The importance ofStefan's flow by collection of insoluble aerosol particles on the surface of the evaporating droplets by condensation has recently been emphasized mainly in connection with the possible wash-out mechanism in the atmosphere. A simple theory is deduced for the collection efficiency of insoluble particles on droplets under theStefan's force and a comparision is made with the binding of aerosol particles byBrown's motion and microturbulence of air flow. In general we must take in account the influence ofStefan's flow by calculating the wash-out efficiency.  相似文献   

14.
Abstract

The flow properties of an homogeneous fluid which is bounded by two concentric spheres and two meridional planes which intersect along a diameter of the spheres are investigated. The spheres rotate about this diameter with slightly different angular velocities. As in the axisymmetric case studied by Proudman (1956) and Stewartson (1966) the viscous terms in the equations of motion are important only in boundary layers on the spheres and on the cylinder C which circumscribes the inner sphere and which has generators parallel to the axis of rotation, provided the Ekman number E is small. In the inviscid region the velocities are independent of the coordinate measuring distance along the axis of rotation and are much weaker, by a factor 0(E ½), than the velocities in the Ekman layer on the driving surface (outer sphere). (It is assumed that the reference frame is fixed in the slower rotating inner sphere.) If the separation of the spheres is small compared to their radii then the asymmetric circulation inside C is characterized by an intense jet along the western wall. Loss of fluid from this jet sustains the eastward and northward flow in the inviscid interior where motion is driven by the suction of the Ekman layer on the outer sphere. (Geophysical conventions have been adopted.) Outside C an intense current is present on the eastern, not western, wall while motion in the inviscid region is westward, and away from the axis of rotation. Though there is no transport across C in the inviscid region, the meridional transport of the Ekman layer on the outer sphere is continuous across C and increases, through suction, as the equator is approached until it drains into an eastward flowing equatorial current of width 0(E 1/7). The eastern boundary current outside C and shear layers on C carry this fluid to the intersection of C and the western wall where it feeds the western boundary current inside C.

The relation between this study and the experiments of Baker and Robinson (1970) is discussed.  相似文献   

15.
Summary A charged particle moves with velocityv in a constant non-uniform magnetic fieldH, spiralling with Larmor radiusR. IfR is small compared with the scale lengthL of the field, the magnetic moment associated with the Larmor motion of the particle is nearly constant. Consequently , the (pitch) angle betweenv andH, varies as arcsinH 1/2. Hence in such adiabatic motion is approximately the same at points on the path whereH has the same value. But the magnetic moment and the pitch angle may differ materially at two such points, each in the region whereR/L is small, if between them the particle traverses a region whereR/L is not small. This region of non-adiabatic motion scatters the pitch angles.Such scattering is investigated for regions of weak field (R large), with and without the presence of a neutral line along whichH=0. Either type of region, it is found, can scatter the pitch angles. This gives support to the theory proposed byAkasofu andChapman to explain why auroral arcs and bands are very thin.The scattering here examined is of interest also in connection with magnetic mirror devices for nuclear energy transformation. It may also have applications to phenomena of solar and stellar atmospheres.  相似文献   

16.
Summary The dynamical response due to the interaction of viscoelastic field and magnetic field in a layer ofVito Volterra's hereditary model is analysed by making use of Laplace-transform.  相似文献   

17.
Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.  相似文献   

18.
Igneous plutons frequently show chemical zoning. The most commonly documented zoning is with the lighter, more silicic, rocks in the centre of the body and the denser, more basic, rocks in the external zone (normal zoning). Less commonly, some plutons show reverse zoning so that the more basic rocks occupy the centre. Widespread evidence shows that zoning in many plutons is the result of interaction between basic and silicic melts.

This work studies, by means of finite difference numerical models, pluton zoning which is due to internal circulation in diapirs comprising two magmas of different composition. Diapirs are modelled here as buoyant isothermal spheres composed of two Newtonian fluids rising through a Newtonian ambient fluid. Ratios of viscosities and densities of the two fluids were varied and the results demonstrated two different styles of internal circulation in rising spheres. The first style, termed “coupled circulation”, is characterised by continuous overturning of both the fluids in a single cell, evolving through both normal and reverse compositional zoning. The overturns stir the fluids and enhance both magma mingling and mixing. Coupled circulation develops in spheres comprising fluids of similar densities and viscosities. As these properties become increasingly different the internal circulation tends to decouple. “Decoupled circulation”, is characterised by circulation of the fluids in two separate cells. Decoupling stops the overturns between the two magmas so that the diapir preserves a reverse zoning throughout its rise, with the denser fluid occupying the central zone. There is less possibility of magma mingling in diapirs undergoing decoupled circulation. Thus, pairs of magmas of similar properties, such as andesite and rhyolite, are most likely to develop coupled circulation leading to both normal and reverse zoning in diapirs; whereas magmas of very different properties, such as basalt and rhyolite, are most likely to decouple resulting in reverse zonation.

The models indicate that reverse zoning would be the most common internal pluton geometry if zoning were controlled by internal circulation alone. Model diapirs which rise along channels of warm, low viscosity wall-rock (hot Stokes' models) or low viscosity shear zones show an increased tendency towards coupled circulation and more intense mechanical stirring of the magmas.  相似文献   


19.
Riassunto Dall'analogia fra il principio ottico diFermat e quello meccanico della minima azione, l'A. ricava un metodo per determinare con mezzi meccanici: 1° la traiettoria di un raggio luminoso passante per due punti dati e separati da un lente; 2°) le superficie di lenti stigmatiche soddisfacenti a condizioni prefissate, in particolare a quelle diAbbe, Herschel.... Si accenna infine a possibili applicazioni nel campo delle lenti sferiche.
Summary From the analogy between the optical principle ofFermat and the mechanical one of minimum action, the Author deduces a method for obtaining with mechanical devices: 1) the optical path of a light beam passing through two given points and separated by a lens; 2) the surfaces of stigmatic lenses fulfilling prefixed conditions, particularly those ofAbbe, Herschell.... Further, it is hinted at possible applications in the field of spherical lenses.
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20.
Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.  相似文献   

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