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1.
—?The number and geometric distribution of putative mantle up-welling centers and the associated convection cell boundaries are determined from the lithospheric plate motions as given by the 14 Euler poles of the observational NUVEL model. For an assumed distribution of up-welling centers (called “cell-cores”) the corresponding cell boundaries are constructed by a Voronoi division of the spherical surface; the resulting polygons are called “Bénard cells.” By assuming the flow-kinematics within a cell, the viscous coupling between the flow and the plates is estimated, and the Euler poles for the plates are computed under the assumption of zero-net-torque. The positions of the cell-cores are optimized for the HS2-NUVEL1 Euler poles by a method of successive approximation (“subplex”); convergence to one of many local minima occurred typically after ～20,000 iterations. Cell-cores associated with the fourteen HS2-NUVEL1 Euler poles converge to a relatively small number of locations (8 to 10, depending on interpretation), irrespective of the number of convection cells submitted for optimized distribution (from 6 to 50). These locations are correlated with low seismic propagation velocities in tomography, uniformly occur within hotspot provinces, and may specifically be associated with the Hawaiian, Iceland, Reunion/Kerguelen (Indian Ocean), Easter Island, Melanesia/Society Islands (South Pacific), Azores/Cape Verde/Canary Islands, Tristan da Cunha (South Atlantic), Balleny Islands, and possibly Yellowstone hotspots. It is shown that arbitrary Euler poles cannot occur in association with mantle Bénard convection, irrespective of the number and the distribution of convection cells. Nevertheless, eight of the observational Euler poles – including the five that are accurately determined in HS2-NUVEL1 (Australia, Cocos, Juan de Fuca, Pacific, and Philippine) – are “Bénard-valid” (i.e., can be explained by our Bénard model). Five of the remaining six observational poles must be relocated within their error-ellipses to become Bénard-valid; the Eurasia pole alone appears to be in error by ～115°, and may actually lie near 40°N, 154°E. The collective results strongly suggest Bénard-like mantle convection cells, and that basal shear tractions are the primary factor in determining the directions of the plate motions as given by the Euler poles. The magnitudes of the computed Euler vectors show, however, that basal shear cannot be the exclusive driving force of plate tectonics, and suggest force contributions (of comparable magnitude for perhaps half of the plates) from the lithosphere itself, specifically subducting slab-pull and (continental) collision drag, which are provisionally evaluated. The relationship of the putative mantle Bénard polygons to dynamic chaos and turbulent flow is discussed. 相似文献
2.
Three-dimensional (3-D) numerical simulations of single turbulent thermal plumes in the Boussinesq approximation are used to understand more deeply the interaction of a plume with itself and its environment. In order to do so, we varied the Rayleigh and Prandtl numbers from Ra?～?105 to Ra?～?108 and from Pr?～?0.025 to Pr?～?70. We found that thermal dissipation takes place mostly on the border of the plume. Moreover, the rate of energy dissipation per unit mass ε T has a critical point around Pr?～?0.7. The reason is that at Pr greater than ～0.7, buoyancy dominates inertia and thermal advection dominates wave formation whereas this trend is reversed at Pr less than ～0.7. We also found that for large enough Prandtl number (Pr?～?70), the velocity field is mostly poloidal although this result was known for Rayleigh–Bénard convection (see Schmalzl et al. [On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 2004, 67, 390--396]). On the other hand, at small Prandtl numbers, the plume has a large helicity at large scale and a non-negligible toroidal part. Finally, as observed recently in details in weakly compressible turbulent thermal plume at Pr?=?0.7 (see Plourde et al. [Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 2008, 604, 99--123]), we also noticed a two-time cycle in which there is entrainment of some of the external fluid to the plume, this process being most pronounced at the base of the plume. We explain this as a consequence of calculated Richardson number being unity at Pr?=?0.7 when buoyancy balance inertia. 相似文献
3.
ABSTRACTThe present study aims to link the dynamics of geophysical fluid flows with their vortical structures in physical space and to study the transition of these structures due to the control parameters. The simulations are carried in a rectangular box filled with liquid gallium for three different cases, namely, Rayleigh–Bénard convection (RBC), magnetoconvection (MC) and rotating magnetoconvection (RMC). The physical setup and material properties are similar to those considered by Aurnou and Olson in their experimental work. The simulated results are validated with theoretical results of Chandrasekhar and experimental results of Aurnou and Olson. The results are also topologically verified with the help of Euler number given by Ma and Wang. For RBC, the onset is obtained at Ra greater than 1708 and at this Ra, the symmetric rolls are orientated in/along a horizontal axis. As the value of Ra increases further, the width of the horizontal rolls starts to amplify. It is observed that these two-dimensional rolls are nothing but the cross-sections of three-dimensional (3D) cylindrical rolls with wave structures. When the vertically imposed magnetic field is added to RBC, the onset of convection is delayed due to the effect of Lorentz force on the thermal buoyancy force. The presence of 3D rectangular structures is highlighted and analysed. When the magnetically influenced rectangular box rotates about vertical axis at low rotation rates in magnetoconvection model, the onset of convection gets further delayed by magnetic field, which is in general agreement with the theoretical predictions. The critical Ra increases linearly with magnetic field intensity. Coherent thermal oscillations are detected near the onset of convection, at moderate rotation rates. 相似文献
4.
Thermal instabilities in the form of oscillatory magnetoconvection representing diffusively modified Alfvén waves in an electrically-conducting Bénard fluid layer of rigid walls in the presence of a vertical magnetic field are investigated. Emphasis of the article is on the transition from a nearly undamped Alfvén wave to diffusively modified Alfvén waves, and on the effect of physically realisable magnetic field boundary conditions on magnetoconvection. It is found that the extra magnetic dissipation in the magnetic Hartmann boundary layers can enhance oscillatory magnetoconvection in the form of strongly modified Alfvén waves. Oscillatory magnetoconvection produced solely by the Alfvén wave mechanism can be the most unstable mode even in the presence of a strong viscous effect. This article also represents the first study on the effect of an electrically conducting wall on magnetoconvection which is associated with a nonlinear eigenvalue problem. We find that the electrically perfectly conducting condition does not yield a good approximation for magnetoconvection with an electrically highly conducting wall. The size of oscillation frequency with an electrically highly conducting wall can be more than a factor of 2 larger than that obtained using the perfectly conducting condition. 相似文献
5.
Richard C. J. Somerville 《地球物理与天体物理流体动力学》2013,107(1):247-262
Abstract The steady nonlinear regime of Bénard convection in a uniformly rotating fluid is treated using a two-dimensional primitive-equation numerical model with rigid boundaries. Quantitative comparisons with laboratory heat transport data for water are made in the parameter ranges for which the experimental flows are approximately two-dimensional and steady. When an experimentally realistic spatial periodicity is imposed upon the numerical solution, the model simulates the experimental determinations of Nusselt number fairly accurately. In particular, it predicts the observed non-monotonic dependence on Taylor number. When spatial periodicities corresponding to those of the linear stability problem are specified, however, the accuracy of the simulation is less and the Taylor number dependence is monotonic. 相似文献
6.
Abstract Chandrasekhar (1961) has summarized the stability results of Bénard convection in a rotating fluid for the cases where the boundary surfaces are both rigid and free, and for both exchange of stabilities and overstability. His analysis provides very accurate results for a limited range of Taylor number J. Bisshopp and Niiler (1965) presented an asymptotic analysis of the rigid boundary problem for exchange of stabilities which is valid for very large Taylor number. The present paper makes use of modern rotating fluid theory to develop an approximate scheme for evaluating the Rayleigh number and other parameters and variables. Known asymptotic results for the free boundary problem at large J are used and an expansion in powers of E1/6 (the Ekman number, E = 2J ?½) yields a sequence of equations and appropriate boundary conditions for the rigid boundary problem. After the algorithm for the calculation is developed, results are given for the problem to second order in the expansion parameter for the case of exchange of stabilities and to first order in the expansion parameters for the overstable case. Ekman boundary layers are important in the development as one might expect. However, an additional, diffusive boundary layer of thickness E? is necessary to provide the details of the temperature field. This boundary layer is the thermal response in the vertical direction to the horizontal spacing of the cells which is also order E?. The horizontal spacing of the cells is essentially a series of contiguous, Stewartson (1957) layers of thickness E?. 相似文献
7.
Abstract Magnetic field generation in a continuous medium in processes without self-excitation—the so-called semi-dynamo, involving as essential elements both magnetohydrodynamic processes and the presence of an impressed e.m.f.—has been studied for the case of the topological pumping effect on the magnetic field generation by an impressed e.m.f. operating in a three-dimensional Bénard convection layer. Under conditions of interest for astrophysical applications the magnetic flux produced can exceed substantially that excited by the e.m.f. in the absence of motion. The results obtained permitted an evaluation of the general quasi-steady magnetic field of the Sun generated by an azimuthal Coriolis e.m.f. which is active in the outermost layers of the convective envelope, taking into account small-scale convective and turbulent motions. In the polar regions of the Sun this field can reach ～10?1 G. 相似文献
8.
Non-linear Rayleigh-Bénard convection in a fluid layer is considered as a model of convection in the Earth's upper mantle. Previous studies have shown that when the temperature is held fixed at one of the boundaries of the layer, convection takes place in cells of width of the order of the layer depth or less. We investigate the effects of a different thermal boundary condition, in which the flux of heat is held fixed on both layer boundaries; then if this flux is just greater than that required for the onset of convection, motion takes place on horizontal scales much greater than the layer depth. An analytical treatment of the equations, based on an expansion in the depth-to-width ratio of the cells, shows that cells of a definite horizontal scale are the fastest growing according to linearised theory, but that these cells are unstable to ones of larger wavelength than themselves. Thus the dominant wavelength lengthens with time. The results hold whether the heat flux is generated internally of comes from beneath the layer. These results produce flow patterns similar to those found when the heat flux is much greater than the critical value. The results have important consequences for the understanding of mantle convection. 相似文献
9.
O. M. Podvigina 《地球物理与天体物理流体动力学》2013,107(4):409-433
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
10.
Jae Min Hyun 《地球物理与天体物理流体动力学》2013,107(1-4):83-98
Abstract An investigation is made of steady thermal convection of a Boussinesq fluid confined in a vertically-mounted rotating cylinder. The top and bottom endwall disks are thermal conductors at temperatures Tt and Tb with δT = Tt ? Tb >0. The vertical sidewall has a finite thermal conductance. A Newtonian heat flux condition is adopted at the sidewall. The Rayleigh number of the fluid system is large to render a boundary layer-type flow. Finite-difference numerical solutions to the full Navier-Stokes equations are obtained. The vertical motions within the buoyancy layer along the sidewall induce weak meridional flows in the interior. Because of the Coriolis acceleration, the meridional flows give rise to azimuthal flows relative to the rotating container. Strong vertical gradients of azimuthal flows exist in the regions near the endwalls. As the stratification effect increases, concentration of flow gradients in thin endwall boundary layers becomes more pronounced. The azimuthal flow field exhibits considerable horizontal gradients. The temperature field develops horizontal variations superposed on the dominant vertical distribution. As either the sidewall thermal conductance or the stratification effect decreases, the temperature distribution tends to the profile varying linearly with height. Comparisons of the sizes of the dynamic effects demonstrate that, in the bulk of flow field, the vertical shear of azimuthal velocity is supported by the horizontal temperature gradient, resulting in a thermal-wind relation. 相似文献
11.
General kinematic implications for plate tectonics are determined for Rayleigh-Bénard convection of the mantle. The continuum of all possible configurations of Bénard polygons is probed by large random samples of global configurations (450,000 to 54,000,000), for each of which the Euler poles are determined on the basis of viscous coupling across the asthenosphere. Two computationally related methods lead first, to Euler pole restrictions for fourteen plates, and second, to restrictions on the Bénard cell configuration. Result No. 1: Euler poles occur in global preference-patterns, which are determined exclusively by the shape of the plate. The observational HS2-NUVEL1 model poles occur near regions preferred by Bénard convection (Eurasia excluded); the agreement is best for the most accurate observational poles. Result No. 2: Seven specific mantle Bénard cells are indicated by present-day plate motions. The upwelling centers correlate with hotspot domains; the major global subduction zones correlate with Bénard model downwelling. This result is independent of the Euler pole accuracy used in its determination, and is consistent with the distribution of low seismic p-wave propagation velocities determined by tomography, and with shear-wave splitting analysis within the asthenosphere. Conclusions: The results suggest that the bulk mantle is divided into less than ten Bénard convection cells globally (cf., Fohlmeister and Renka, 2002), each of which extends from the asthenosphere to the core-mantle boundary; turbulent flow, and other perturbations of the Bénard kinematics appear to be limited. These primally poloidal flow kinematics provide basal shear forces as a major component in driving plate tectonics, and are specifically configured for the directions of plate motions. The Bénard model is incomplete without a dynamic contribution from the lithosphere, which represents a separate convection layer of the distinct polar kinematics of rigid plates. The complete hybrid mechanism for driving plate tectonics includes lithospheric buoyancy dynamics, specifically from the subducting Pacific plate slabs to compensate for plate-slowing due to the back-flow sector of the Hawaiian convection cell, and collision-drag dynamics principally for smaller plates or continental margins. 相似文献
12.
Abstract We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983). We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δvy exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber ka are damped over a timescale kuRe 0|δ vy/vA |?2, Re 0 being the Reynolds number corresponding to the Braginskij viscosity coefficient η0 and vA the Alfvén speed. Dissipation is most effective where β = (vs /vA) 2 ≈ 1, vs being the speed of sound. 相似文献
13.
Benoit Cushman-Roisin 《地球物理与天体物理流体动力学》2013,107(1-2):35-59
Abstract A new model of convection and mixing is presented. The fluid is envisioned as being composed of two buoyant interacting fluids, called thermals and anti-thermals. In the context of the Boussinesq approximation, pairs of governing equations are derived for thermals and anti-thermals. Each pair meets an Invariance Principle as a consequence of the reciprocity in the roles played by thermals and anti-thermals. Each pair is transformed into an average equation for which interaction terms cancel and another very simple equation linking the two fluid properties. An important parameter of the model is the fraction, f, of area occupied by thermals to the total area. A dynamic saturation equilibrium between thermals and antithermals is assumed. This implies a constant values of f throughout the system. The set of equations is written in terms of mean values and root-mean-square fluctuations, in keeping with equations of turbulence theories. The final set consists of four coupled non-linear differential equations. The model neglects dissipation and can be applied to any convective situations where molecular viscosity and diffusivity may be neglected. Applications of the model to mixed-layer deepening and penetrative convection are presented in subsequent papers. 相似文献
14.
J. Boda 《地球物理与天体物理流体动力学》2013,107(1-4):77-90
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
15.
Abstract The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow. 相似文献
16.
Abstract Numerical simulations of internal gravity waves-turbulence are carried out for the inviscid, viscous and forced-dissipative two-dimensional primitive equations using the spectral method. Some of the results are compared with the predictions of the eddy damped quasi-normal Markovian (EDQNM) closure for internal waves of Carnevale and Frederiksen, generalized for periodic boundary conditions and possible random forcing and dissipation. The EDQNM reduces to the Boltzman equation of resonant interaction theory in the continuum space limit and as the forcing and dissipation vanish. However, the limit is singular in the sense that as well as conserving total energy, E, and total cross-correlation between the vorticity and buoyancy fields, C, an additional conservation law, viz. z-momentum, Pz , occurs in the limit. This means that the resonant interaction equilibrium (RIE) solution of the Boltzmann equation differs from the statistical mechanical equilibrium (SME) solution of the EDQNM closure. The statistical stability of the SME and RIE spectra for the primitive equations is tested by integrating the inviscid equations using initial realizations of these spectra with random phases. It is found that E and C are accurately conserved while Pz undergoes large amplitude variations. The approach to equilibrium of initial disequilibrium spectra is monitored by examining the evolution of the entropy. The increase and asymptotic approach to a constant value corresponding to complete chaos is consistent with the behaviour predicted by the EDQNM closure. For the viscous decay and forced-dissipative experiments, the behaviour of the entropy is also consistent with that predicted by the EDQNM closure. There is approximate equipartition of potential and total kinetic energies throughout the integrations from initial conditions having equal potential and total kinetic energies and as well equal vertical and horizontal energies, but as expected, the ratio of horizontal to vertical kinetic energy increases with time to a value greater than unity. With Laplacian viscous dissipation and thermal diffusivity, the statistical steady states produced in the forced-dissipative experiments have k?3 power laws for k≧7. A comparison with the power laws for kinetic energy and passive scalar variance produced in a numerical simulation of the two-dimensional passive scalar problem is also presented. 相似文献
17.
We study the effect of stratification and compressibility on the threshold of convection and the heat transfer by developed convection in the nonlinear regime in the presence of strong background rotation. We consider fluids both with constant thermal conductivity and constant thermal diffusivity. The fluid is confined between two horizontal planes with both boundaries being impermeable and stress-free. An asymptotic analysis is performed in the limits of weak compressibility of the medium and rapid rotation (τ?1/12???|θ|???1, where τ is the Taylor number and θ is the dimensionless temperature jump across the fluid layer). We find that the properties of compressible convection differ significantly in the two cases considered. Analytically, the correction to the characteristic Rayleigh number resulting from small compressibility of the medium is positive in the case of constant thermal conductivity of the fluid and negative for constant thermal diffusivity. These results are compared with numerical solutions for arbitrary stratification. Furthermore, by generalizing the nonlinear theory of Julien and Knobloch [Fully nonlinear three-dimensional convection in a rapidly rotating layer. Phys. Fluids 1999, 11, 1469–1483] to include the effects of compressibility, we study the Nusselt number in both cases. In the weakly nonlinear regime we report an increase of efficiency of the heat transfer with the compressibility for fluids with constant thermal diffusivity, whereas if the conductivity is constant, the heat transfer by a compressible medium is more efficient than in the Boussinesq case only if the specific heat ratio γ is larger than two. 相似文献
18.
《Advances in water resources》1998,21(5):401-425
This work continues the analysis of variable density flow in groundwater systems. It focuses on both thermohaline (double-diffusive) and three-dimensional (3D) buoyancy-driven convection processes. The finite-element method is utilized to tackle these complex non-linear problems in two and three dimensions. The preferred numerical approaches are discussed regarding appropriate basic formulations, balance-consistent discretization techniques for derivative quantitites, extension of the Boussinesq approximation, proper constraint conditions, time marching schemes, and computational strategies for solving large systems. Applications are presented for the thermohaline Elder and salt dome problem as well as for the 3D extension of the Elder problem with and without thermohaline effects and a 3D Bénard convection process. The simulations are performed by using the package FEFLOW. Conclusions are drawn with respect to numerical efforts and the appropriateness for practical needs. 相似文献
19.
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 zr (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. 相似文献
20.
David E. Loper 《地球物理与天体物理流体动力学》2013,107(1):133-156
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/E½ ? δ ? α2/E, spin-up by meridional circulation of current with weak Alfvén waves; 1 ? δ ? α/E½, spin-up by strong Alfvén waves; α½/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. 相似文献