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1.
Abstract

In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B 2/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 1014cm2s?1, which is an order of magnitude larger than usually adopted in solar mean field models.  相似文献   

2.

A linear analysis of thermally driven magnetoconvection is carried out with emphasis on its application to convection in the Earth's core. We consider a rotating and self-gravitating fluid sphere (or spherical shell) permeated by a uniform magnetic field parallel to the spin axis. In rapidly rotating cases, we find that five different convective modes appear as the uniform field is increased; namely, geostrophic, polar convective, magneto-geostrophic, fast magnetostrophic and slow magnetostrophic modes. The polar convective (P) and magneto-geostrophic (E) modes seem to be of geophysical interest. The P mode is characterized by such an axisymmetric meridional circulation that the fluid penetrates the equatorial plane, suggesting that generation of quadrapole from dipole fields could be explained by a linear process. The E mode is characterized by a few axially aligned columnar rolls which are almost two-dimensional due to a modified Proudman-Taylor theorem.  相似文献   

3.
Abstract

A meridional circulation of sunspots has been measured through the digital analysis of the Meudon spectroheliograms from 1978 to 1983. Old and young sunspots follow a zonal meridional circulation, in several bands of latitude, in which two adjacent bands have opposite motions. This meridional circulation pattern is time-dependent. Using the H α filaments as magnetic field tracers, a large-scale magnetic pattern has been found that was also obtained independently by direct measurement of the magnetic field (Hoeksema, 1988).

The coincidence of a large-scale magnetic pattern with a zonal meridional circulation suggests the existence of azimuthal rolls below the surface, and these azimuthal rolls can explain a number of properties of the solar cycle. New rolls occur with increasing proximity to the Equator, thereby indicating the direction of propagation of the dynamo wave. The occurrence of rolls is very favorable to the emergence of the magnetic regions. The rolls also influence the magnetic complexity of the active regions. They modulate the surface rotation through the Coriolis force, which accelerates or decelerates the fluid particles. They therefore offer a plausible explanation of the torsional oscillation pattern.

There are a number of problems raised by such an unexpected circulation pattern: for example, the coexistence of axisymmeric rolls with hypothetical giant cells, the location of the dynamo source below or within the convective zone, and the coupling of the radiative interior and the convective layers. To resolve these important issues, continuous observational studies are needed of the manifestation of solar activity, as well as of radius and luminosity variations. So, we have aimed our paper at an audience of theoreticians in the hope that they take up the challenges we describe.  相似文献   

4.
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   

5.
Numerous studies of magnetic fluctuations with a zero mean-field for small magnetic Prandtl numbers (Pr m 1) show that magnetic fluctuations cannot be generated by turbulent fluid flow with the Kolmogorov energy spectrum. In addition, the generation of magnetic fluctuations with a zero mean-field for Pr m 1 were not observed in numerical simulations. However, in astrophysical plasmas the magnetic Prandtl numbers are small and magnetic fluctuations are observed. Thus a mechanism of generation of magnetic fluctuations for Pr m 1 still remains poorly understood. On the other hand, in astrophysical applications (e.g., solar and stellar convection zones, galaxies, accretion disks) the turbulent velocity field cannot be considered as a divergence-free. The generation of magnetic fluctuations by turbulent flow of conducting fluid with a zero mean magnetic field for Pr m 1 is studied by means of linear and nonlinear analysis. The turbulent fluid velocity field is assumed to be homogeneous and isotropic with a power law energy spectrum ( k –p ) and with a very short scale-dependent correlation time. It is found that magnetic fluctuations can be generated when the exponent p > 3/2. It is shown also that the growth rates of the higher moments of the magnetic field are larger than those of the lower moments, i.e., the spatial distribution of the magnetic field is intermittent. In addition, the effect of compressibility (i.e., u 0) of the low-Mach-number turbulent fluid flow u is studied. It is demonstrated that the threshold for the generation of magnetic fluctuations by turbulent fluid flow with u 0 is higher than that for incompressible fluid. This implies that the compressibility impairs the generation of magnetic fluctuations. Nonlinear effects result in saturation of growth of the magnetic fluctuations. Asymptotic properties of the steady state solution for the second moment of the magnetic field in the case of the Hall nonlinearity for the low-Mach-number compressible flow are studied.  相似文献   

6.
Summary The present paper deals with a hydromagnetic dynamo model of the generation mechanism of the Earth's magnetic field. An attempt has been made at selecting a flow-velocity field in the Earth's core which would satisfy the condition 0 for regenerating the field according to [2], and which would yield a velocity field pattern on the core surface as given in the papers by Kahle et al. [9]. These conditions are satisfied by the velocityv=V 1+U 2 c –V 2 c and, geometrically, this velocity field is represented in space by a spiral convective motion. On the core surface two downflows and two upflows with the corresponding rotating cells may then be found. Only the axisymmetric harmonic component regeneration of the magnetic field has been considered. Adequate regeneration equations have been obtained by means of Braginski's method of quantity estimates in order of magnitude.  相似文献   

7.
Abstract

We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD 0, and the other for |D| ? 1. Asymptotic solutions for |D—D 0| ? |D 0| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|?s) for |B| → ∞, we demonstrate that |B| = O(|D|1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.  相似文献   

8.
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 Rc for a wide class of parameters. Here, Rc is typically much less than in the case of a single layer, although the scaling Rc～T2/3 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.  相似文献   

9.
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10.
Abstract

Dynamo action in a highly conducting fluid with small magnetic diffusivity η is particularly sensitive to the topology of the flow. The sites of rapid magnetic field regeneration, when they occur, appear to be located at the stagnation points or in regions where the particle paths are chaotic. Elsewhere only slow dynamo action is to be expected. Two such examples are the nearly axially symmetric dynamo of Braginsky and the generalisation to smooth velocity fields of the Ponomarenko dynamo. Here a method of solution is developed, which applies to both these examples and is applicable to other situations, where magnetic field lines are close to either closed or spatially periodic contours. Particular attention is given to field generation in the neighbourhood of resonant surfaces where growth rates may be intermediate between the slow diffusive and fast convective time scales. The method is applied to the case of the two-dimensional ABC-flows, where it is shown that such intermediate dynamo action can occur on resonant surfaces.  相似文献   

11.
Abstract

We consider the turbulent dynamo action in a differentially rotating flow by making use of a kinematic approach when the effect of a generated magnetic field on turbulent motions is neglected. The mean electromotive force is calculated in a quasilinear approximation. Differential rotation can stretch turbulent magnetic field lines and break the symmetry of turbulence in such a way that turbulent motions become suitable for the generation of a large scale magnetic field. The presence of shear changes the type of an equation governing the mean magnetic field. Due to shear stresses the mean magnetic field can be generated by a turbulent dynamo action even in a uniform turbulence. The growth rate depends on the length scale of the mean field being faster for the field with a smaller length scale.  相似文献   

12.
Abstract

We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema.

The general method is illustrated by the global asymptotic solution of the α2-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified.

Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability using comparisons with complementary asymptotic expansions and numerical simulations. In particular, this justifies application of the MEGA solutions to estimation of the generation threshold.  相似文献   

13.
Abstract

Fluxes of angular momentum produced by turbulence in rotating fluids are derived with the effects of a magnetic field included. It is assumed that the rotation is slow but that the magnetic field is of arbitrary strength. A mean magnetic field is shown to produce qualitative changes of the sources of the differential rotation rather than the quenching of differential rotation usually expected. A new equatorward flux of angular momentum arises through the influence of the toroidal magnetic field. The possibility of interpreting the torsional oscillations of the Sun as a consequence of the magnetic perturbations of the turbulent angular momentum fluxes is discussed.  相似文献   

14.
Abstract

The concept of “catchment-scale storm velocity” quantifies the rate of storm motion up and down the basin accounting for the interaction between the rainfall space–time variability and the structure of the drainage network. It provides an assessment of the impact of storm motion on flood shape. We evaluate the catchment-scale storm velocity for the 29 August 2003 extreme storm that occurred on the 700 km2-wide Fella River basin in the eastern Italian Alps. The storm was characterized by the high rate of motion of convective cells across the basin. Analysis is carried out for a set of basins that range in area from 8 to 623 km2 to: (a) determine velocity magnitudes for different sub-basins; (b) examine the relationship of velocity with basin scale and (c) assess the impact of storm motion on simulated flood response. Two spatially distributed hydrological models of varying degree of complexity in the representation of the runoff generation processes are used to evaluate the effects of the storm velocity on flood modelling and investigate model dependencies of the results. It is shown that catchment-scale storm velocity has a non-linear dependence on basin scale and generally exhibits rather moderate values, in spite of the strong kinematic characteristics of individual storm elements. Consistently with these observations and for both models, hydrological simulations show that storm motion has an almost negligible effect on the flood response modelling.

Editor Z.W. Kundzewicz; Guest editor R.J. Moore

Citation Nikolopoulos, E.I., Borga, M., Zoccatelli, D., and Anagnostou, E.N., 2014. Catchment-scale storm velocity: quantification, scale dependence and effect on flood response. Hydrological Sciences Journal, 59 (7), 1363–1376. http://dx.doi.org/10.1080/02626667.2014.923889  相似文献   

15.
Abstract

We investigated global axisymmetric (m = 0) and non-axisymmetric (m = 1) modes of magnetic fields generated by the galactic dynamo including the α2-dynamo. The α2-dynamo is responsible for the field generation in the central region of galaxies where the shear of galactic rotation is weak (e.g. M51). The highest growth rate of m = 1 modes is always smaller than that of m = 0 modes; thus m = 1 modes of the standard galactic dynamo cannot explain the dominance of the bisymmetric fields in spiral galaxies. Radial extent of each m = 1 mode is too narrow to reproduce the observed bisymmetric structure extending over a disk.  相似文献   

16.
Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B 0, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 105 have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B 0 with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.  相似文献   

17.
Abstract

Evapotranspiration rates determined from meteorological data by the Bowen ratio method were tested against rates obtained from weighing lysimeters. The tests were conducted on an irrigated field (73 by 92 meters), where the minimum fetch was 27 m. Air-temperature and vapor-pressure differences obtained as 15-minute averages at heights of from 5 to 40 cm above the crop surface were used to calculate evapotranspiration. The results indicate that the Bowen ratio method can be used successfully to determine the evaporative flux for short periods, which can be summed for longer periods. During daylight periods, the absolute errors were less that. 0.02 cal cm?2 min?1 (or ly min?1), while the relative errors were less than 5 percent.  相似文献   

18.
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   

19.
Abstract

The weak-field Benard-type dynamo treated by Soward is considered here at higher levels of the induced magnetic field. Two sources of instability are found to occur in the intermediate field regime M ～ T 1/12, where M and T are the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time owing to destabilization of the convection by the magnetic field. On a faster time scale a dynamic instability related to MAC-wave instability can also occur. It is therefore concluded that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy.

In an attempt to model stabilization of the dynamo in a strong-field regime we consider two approximations. In the first, a truncated expansion in three-dimensional plane waves is studied numerically. A second approach utilizes an ad hoc set of ordinary differential equations which contains many of the features of convection dynamos at all field energies. Both of these models exhibit temporal intermittency of the dynamo effect.  相似文献   

20.
Abstract

A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.  相似文献   

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