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1.
Abstract

The mean-field effects of cyclonic convection become increasingly complex when the cyclonic rotation exceeds ½-π. Net helicity is not required, with negative turbulent diffusion, for instance, appearing in mirror symmetric turbulence. This paper points out a new dynamo effect arising in convective cells with strong asymmetry in the rotation of updrafts as against downdrafts. The creation of new magnetic flux arises from the ejection of reserve flux through the open boundary of the dynamo region. It is unlike the familiar α-effect in that individual components of the field may be amplified independently. Several formal examples are provided to illustrate the effect. Occurrence in nature depends upon the existence of fluid rotations of the order of π in the convective updrafts. The flux ejection dynamo may possibly contribute to the generation of field in the convective core of Earth and in the convective zone of the sun and other stars.  相似文献   

2.
An axisymmetric model of convection in a rotating cylinder in an external uniform magnetic field has been considered. In the considered model, the meridional circulation is created by a nonuniform rotation of the lower boundary relative to the other boundaries. In the considered model, the time of formation of the stationary regime in the magnetic field considerably increases if the vertical density (compressibility) inhomogeneity is taken into account for Ekman numbers of E = E M = 3 × 10−3. This example shows that the compressibility of a medium should be taken into account in the convection and dynamics of the magnetic field when the magnetohydrodynamics of the Earth is analyzed.  相似文献   

3.
Thermal convection in the mantle is caused by the heat transported upwards from the core and by the heat produced by the internal radioactive sources. According to the data on the heat transfer by the mantle plumes and geochemical evidence, only 20% of the total heat of the Earth is supplied to the mantle from the core, whereas most of the heat is generated by the internal sources. Along with the models that correctly allow for the internal heat sources, there are also many publications (including monographs) on the models of mantle convection that completely ignore the internal heating or the heat flux from below. In this study, we analyze to what extent these approximations could be correct. The analytical distributions of temperature and heat flux in the case of internal heating without convection and the results of the numerical modeling for convection with different intensity are presented. It is shown that the structure of thermal convection is governed by the distribution of the heat flux in the mantle but not by the heat balance, as it is typically implicitly assumed in most works. Heat production by the internal sources causes the growth of the heat flux as a function of radius. However, in the spherical mantle of the Earth, the heat flux decreases with radius due to the geometry. It turned out that with the parameters of the present Earth, both these effects compensate each other to a considerable extent, and the resulting heat flux turns out to be nearly constant as a function of radius. Since the structure of the convective flows in the mantle is determined by the distributions of heat flux and total heat flux, in the Cartesian models of the mantle convection the effective contribution of internal heating is small, and ignoring the heat flux from the core significantly distorts the structure of the convective currents and temperature distributions in the mantle.  相似文献   

4.
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   

5.
Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.  相似文献   

6.
Unstable density‐driven groundwater flow and solute transport (i.e., free convection) leads to spatiotemporal variations in pressure. Specific storage (So) indicates the capability of a confined aquifer to release or store groundwater associated with a pressure change. Although So is known to dampen pressure propagation, So has been implicitly assumed to have a negligible impact on the unstable free convective process in prior studies. This work explores the effect of So on both the classic onset criterion and the fingering process using numerical models. Results show that the classic onset criterion is applicable when So is smaller than 10–1 m–1. Results also demonstrate that So does not play a significant role in the free convective fingering process unless it is greater than 10–3 m–1. For most practical purposes in hydrogeology (large Rayleigh number and small So), the implicit assumption of small or zero So is appropriate.  相似文献   

7.
Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 105, Prandtl number P = 1, and Rayleigh number R between 1 |MX 104 and 4 |MX 104 (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 104, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 104, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 104, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 104, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 104, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 104 maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 104.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.  相似文献   

8.
Interhemispheric contrasts in the ionospheric convection response to variations of the interplanetary magnetic field (IMF) and substorm activity are examined, for an interval observed by the Polar Anglo-American Conjugate Experiment (PACE) radar system between 1600 and 2100 MLT on 4 March 1992. Representations of the ionospheric convection pattern associated with different orientations and magnitudes of the IMF and nightside driven enhancements of the auroral electrojet are employed to illustrate a possible explanation for the contrast in convection flow response observed in radar data at nominally conjugate points. Ion drift measurements from the Defence Meteorological Satellite Program (DMSP) confirm these ionospheric convection flows to be representative for the prevailing IMF orientation and magnitude. The location of the fields of view of the PACE radars with respect to these patterns suggest that the radar backscatter observed in each hemisphere is critically influenced by the position of the ionospheric convection reversal boundary (CRB) within the radar field of view and the influence it has on the generation of the irregularities required as scattering targets by high-frequency coherent radar systems. The position of the CRB in each hemisphere is strongly controlled by the relative magnitudes of the IMF Bz and By components, and hence so is the interhemispheric contrast in the radar observations.  相似文献   

9.
Natural convection in magmas at subliquidus temperatures is analyzed using Bingham plastic and power-law rheology models. Heat flux measurements were obtained at liquidus and subliquidus temperatures for degassed basaltic lava at atmospheric pressure. These measurements of heat flux ranged from 2 to 40 kW/m2 and were obtained using two different types of convective heat flux probes. The agreement between the two different instruments and the theoretical calculations is excellent. A noticeable change in the trend of the convective heat flux data is observed in the vicinity of the liquidus temperature. Subliquidus convective heat flux rates (6–15 kW/m2) are attractive for energy extraction applications.  相似文献   

10.
We document the detailed dynamics of the dayside aurora in the ≈1200–1600 MLT sector in response to a sharp southward turning of the interplanetary magnetic field (IMF) under negative IMF By conditions. Features not documented in previous work are elucidated by using two meridan scanning photometers (separated by 2 h) and an all-sky auroral imager in Ny Ålesund, Svalbard (75.5^MLAT) in combination with magnetograms from stations on Svalbard, covering the latitude range 71^–75^MLAT. The initial auroral response may be divided into three phases consisting of: (1) intensification of both the red (630.0 nm) and green (557.7 nm) line emissions in the cusp aurora near 1200 MLT and ≈100 km equatorward shift of its equatorward boundary, at ≈75^MLAT, (2) eastward and poleward expansions of the cusp aurora, reaching the 1430 MLT meridian after 5–6 min, and (3) east-west expansion of the higher-latitude aurora (at ≈77^–78^MLAT) in the postnoon sector. The associated magnetic disturbance is characterized by an initial positive deflection of the X-component at stations located 100–400 km south of the aurora, corresponding to enhanced Sunward return flow associated with the merging convection cell in the post-noon sector. The sequence of partly overlapping poleward moving auroral forms (PMAFs) during the first 15 min, accompanied by corresponding pulsations in the convection current, was followed by a strong westward contraction of the cusp aurora when the ground magnetograms indicated a temporary return to the pre-onset level. These observations are discussed in relation to the Cowley-Lockwood model of ionospheric response to pulsed magnetopause reconnection.  相似文献   

11.
The effects of rotation and a toroidal magnetic field on the preferred pattern of small amplitude convection in spherical fluid shells are considered. The convective motions are described in terms of associated Legendre functions Pl|m| (cos θ). For a given pair of Prandtl number P and magnetic Prandtl number Pm the physically realized solution is represented either by m = 0 or |m| = l depending on the ratio of the rotation rate Λ to the magnetic field amplitude H. The case of m = 0 is preferred if this ratio ranges below a critical value, which is a function of the shell thickness, and |m| = l otherwise.  相似文献   

12.
The problem of the transport and transformation of magnetic fields from the generation zone to the photosphere is studied in this paper. For this purpose, the temporal variations of parameters of bipolar magnetic regions are analyzed based on the magnetic synoptic maps of the Wilcox Solar Observatory (WSO) for the declining phase of cycle 22. A 150-day modulation of the magnetic flux value in bipolar regions and a variation in their rotation velocity with a duration of 80–100 days have been found. Such variations in the parameters are interpreted as a result of action of supergiant and giant convection cells. The magnetic flux from the generation zone emerges through the local channels formed by the supergiant convection cells. From the level of 0.95 RSun, the flux is redistributed by giant cells, which form bipolar magnetic regions on the photosphere.  相似文献   

13.
Nonlinear disturbance of the dipole field by nonaxisymmetric plasma pressure distribution was analyzed under the assumption of magnetostatic equilibrium for finite values of the plasma parameter at the pressure maximum area. The distributions of isolines of the constant value of magnetic-field component B Z and the volume of magnetic flux tube in the equatorial plane were obtained. At a finite plasma pressure, local minima and maxima of the magnetic field are formed. The formation of these local maxima and minima leads to the formation of contours (not surrounding the Earth) B min = const, where B min is the minimum magnetic field on the magnetic field line. This changes the direction of the gradient of the volume of the magnetic flux tube. The configuration of appearing field-aligned currents was determined. The results obtained are discussed in terms of their use in explaining a number of effects observed in the Earth’s magnetosphere.  相似文献   

14.
Abstract

An exceptional case to the model-independent theory of Knobloch (1995) is presented, by investigating a rotating cylindrical annulus of height H and side wall radii r o and r i, with non-slip, perfectly thermally conducting side walls and thermally insulating stress-free ends. Radial heating permits the possibility of either two- or three-dimensional convective solutions being the preferred mode. An analytical solution is obtained for the two-dimensional case and a numerical solution for the three-dimensional solution, which is also applied to the two-dimensional solution. It is shown that both two- and three-dimensional solutions can be realized depending on the aspect ratio, γ = H/d, where d = r o-r i is the thickness of the annulus, the radii ratio λ = r i/r o and the rotation rate of the model. For γ = O(1) and λ = 0.4, the preferred convective solution is three-dimensional when the Taylor number, T < 102 and two-dimensional for T > 102. For small aspect ratios, γ ? 1, the preferred mode is two-dimensional for all rotation rates.  相似文献   

15.
We investigate the dayside auroral dynamics and ionospheric convection during an interval when the interplanetary magnetic field (IMF) had predominantly a positive Bz component (northward IMF) but varying By. Polar UVI observations of the Northern Hemisphere auroral emission indicate the existence of a region of luminosity near local noon at latitudes poleward of the dayside auroral oval, which we interpret as the ionospheric footprint of a high-latitude reconnection site. The large field-of-view afforded by the satellite-borne imager allows an unprecedented determination of the dynamics of this region, which has not previously been possible with ground-based observations. The location of the emission in latitude and magnetic local time varies in response to changes in the orientation of the IMF; the cusp MLT and the IMF By component are especially well correlated, the emission being located in the pre- or post-noon sectors for By < 0 nT or By > 0 nT, respectively. Simultaneous ground-based observations of the ionospheric plasma drift are provided by the CUTLASS Finland HF coherent radar. For an interval of IMF By 0 nT, these convection flow measurements suggest the presence of a clockwise-rotating lobe cell contained within the pre-noon dayside polar cap, with a flow reversal closely co-located with the high-latitude luminosity region. This pattern is largely consistent with recent theoretical predictions of the convection flow during northward IMF. We believe that this represents the first direct measurement of the convection flow at the imaged location of the footprint of the high-latitude reconnection site.  相似文献   

16.
Abstract

The linear hydromagnetic stability of a non-constantly stratified horizontal fluid layer permeated by an azimuthal non-homogeneous magnetic field is investigated for various widths of the stably stratified part of the layer in the geophysical limit q→0 (q is the ratio of thermal and magnetic diffusivities). The choice of the strength of the magnetic field Bo is as in Soward (1979) (see also Soward and Skinner, 1988) and the equations for the disturbances are treated as in Fearn and Proctor (1983). It was found that convection is developed in the whole layer regardless of the width of its stably stratified part. The thermal instability penetrates essentially from the unstably stratified part of the layer into the stably stratified part for A ～ 1 (A characterises the ratio of the Lorentz and Coriolis forces). When the magnetic field is strong (A>1) the thermal convection is suppressed in the stably stratified part of the layer. However, in this case, it is replaced by the magnetically driven instability; which is fully developed in the whole layer. The thermal instabilities always propagate westward and exist for all the modes m. The magnetically driven instabilities propagate either westward or eastward according to the width of the stably and unstably stratified parts and exist only for the mode m=1.  相似文献   

17.
Investigation of magnetic field generation by convective flows is carried out for three values of kinematic Prandtl number: P = 0.3, 1 and 6.8. We consider Rayleigh–Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period in the x and y directions. Convective attractors are modelled for increasing Rayleigh numbers for each value of the kinematic Prandtl number. Linear and non-linear dynamo action of these attractors is studied for magnetic Prandtl numbers P m ≤ 100. Flows, which can act as magnetic dynamos, have been found for all the three considered values of P, if the Rayleigh number R is large enough. The minimal R, for which of magnetic field generation occurs, increases with P. The minimum (over R) of critical Pm for magnetic field generation in the kinematic regime is admitted for P = 0.3. Thus, our study indicates that smaller values of P are beneficial for magnetic field generation.  相似文献   

18.
Abstract

The solution of the full nonlinear hydromagnetic dynamo problem is a major numerical undertaking. While efforts continue, supplementary studies into various aspects of the dynamo process can greatly improve our understanding of the mechanisms involved. In the present study, the linear stability of an electrically conducting fluid in a rigid, electrically insulating spherical container in the presence of a toroidal magnetic field Bo(r,θ)lø and toroidal velocity field Uo(r,θ)lø, [where (r,θ,ø) are polar coordinates] is investigated. The system, a model for the Earth's fluid core, is rapidly rotating, the magnetostrophic approximation is used and thermal effects are excluded. Earlier studies have adopted a cylindrical geometry in order to simplify the numerical analysis. Although the cylindrical geometry retains the fundamental physics, a spherical geometry is a more appropriate model for the Earth. Here, we use the results which have been found for cylindrical systems as guidelines for the more realistic spherical case. This is achieved by restricting attention to basic states depending only on the distance from the rotation axis and by concentrating on the field gradient instability. We then find that our calculations for the sphere are in very good qualitative agreement both with a local analysis and with the predictions from the results of the cylindrical geometry. We have thus established the existence of field gradient modes in a realistic (spherical) model and found a sound basis for the study of various other, more complicated, classes of magnetically driven instabilities which will be comprehensively investigated in future work.  相似文献   

19.
Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere (‘convective collapse’) are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 105 G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.  相似文献   

20.
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