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1.
This article addresses the interesting and important problem of large-scale magnetic field generation in turbulent flows, using a self-consistent dynamo model recently developed. The main idea of this model is to consider the induction equation for the large-scale magnetic field, integrated consistently with the turbulent dynamics at smaller scales described by a magnetohydrodynamic shell model. The questions of dynamo action threshold, magnetic field saturation, magnetic field reversals, nature of the dynamo transition and the changes of small-scale turbulence as a consequence of the dynamo onset are discussed. In particular, the stability curve obtained by the model integration is shown in a very wide range of values of the magnetic Prandtl number not yet accessible by direct numerical simulation but more realistic for natural dynamos. Moreover, from our analysis it is shown that the large-scale dynamo transition displays a hysteretic behaviour and therefore a subcritical nature. The model successfully reproduces magnetic polarity reversals, showing the capability to generate persistence times which are increasing for decreasing magnetic diffusivity. Moreover, when the system reaches a statistically stationary dynamo state, where the large-scale magnetic field can abruptly reverse its polarity (magnetic reversal state) or not, keeping the same polarity (steady state), it shows an unmistakable tendency towards the energy equipartition for the turbulence at small scale.  相似文献   

2.
Large eddy simulations (LES) of two-dimensional turbulent convection within the anelastic approximation are presented for Rayleigh number Ra?=?109, Prandtl number Pr?=?1 with free-slip boundary conditions. Various subgrid-scale (SGS) models are investigated such as a similarity model, a dynamic similarity model, a dynamic eddy-viscosity model, a hyperdiffusion model and a hybrid model (dynamic similarity hyperdiffusion model). To study the effects of density stratification on the models, we have also carried out simulations for a Boussinesq flow. The SGS models are compared to direct numerical simulation (DNS) data on the basis of kinetic energy and entropy variance spectra, mean entropy profiles, r.m.s. entropy profiles and r.m.s. kinetic energy density profiles. The results show that for the Boussinesq flow, all the SGS models agree fairly well with the high resolution DNS data. However, for the strongly density-stratified flow, only the hyperdiffusion and the hybrid model show good performance.  相似文献   

3.
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   

4.
Over the past 10 years, geodynamo simulations have grown rapidly in sophistication. However, it is still necessary to make certain approximations in order to maintain numerical stability. In addition, models are forced to make assumptions about poorly known parameters for the Earth's core. Different magnetic Prandtl numbers have been used and different assumptions about the presence of radiogenic heating have been made. This study examines some of the consequences of different approximations and assumptions using the Glatzmaier–Roberts geodynamo model. Here, we show that the choice of magnetic Prandtl number has a greater influence on the character of the magnetic field produced than the addition of a plausible amount of radiogenic heating. In particular, we find that prescribing a magnetic Prandtl number of unity with Ekman number limited by current computing resources, results in magnetic fields with significantly smaller intensities and variabilities compared with the much more Earth-like results obtained from simulations with large magnetic Prandtl numbers. A magnetic Prandtl number of unity, with both the viscous and magnetic diffusivities set to the Earth's magnetic diffusivity, requires a rotation rate much smaller than that of the Earth for currently reachable Ekman numbers. This results in a reduced dominance of the Coriolis forces relative to the buoyancy forces, and therefore, a reduction in the magnetic field intensity and the variability compared to the large Prandtl number cases.  相似文献   

5.
In the present project we investigate the evolution of a three-dimensional (3D), large-scale galactic magnetic field under the influence of gas flows in spiral arms and in the presence of dynamo action. Our principal goal is to check how the dynamical evolution of gaseous spiral arms affects the global magnetic field structure and to what extent our models could explain the observed spiral patterns of polarization B-vectors in nearby galaxies. A two-step scheme is used: the N-body simulations of a two-component, self-gravitating disk provide the time-dependent velocity fields which are then used as the input to solve the mean-field dynamo equations. We found that the magnetic field is directly influenced by large-scale non-axisymmetric density wave flows yielding the magnetic field locally well-aligned with gaseous spiral arms in a manner similar to that discussed already by Otmianowska-Mazur et al. 1997. However, an additional field amplification, introduced by a non-zero -term in the dynamo equations, is required to cause a systematic increase of magnetic energy density against the diffusive losses. Our simulated magnetic fields are also used to construct the models of a high-frequency (Faraday rotation-free) polarized radio emission accounting for effects of projection and limited resolution, thus suitable for direct comparisons with observations.  相似文献   

6.
We study generation of magnetic fields, involving large spatial scales, by convective plan-forms in a horizontal layer. Magnetic modes and their growth rates are expanded in power series in the scale ratio, and the magnetic eddy diffusivity (MED) tensor is derived for flows, symmetric about the vertical axis in a layer. For convective rolls we demonstrate that MED is never below molecular magnetic diffusivity. For cell patterns possessing the symmetries of a rectangle, critical values of molecular magnetic diffusivity for the onset of small- and large-scale magnetic field generation are the same. No instances of negative MED in hexagonal cells have been detected. A family of plan-forms has been found numerically, where MED is negative for molecular magnetic diffusivity over the threshold for the onset of small-scale magnetic field generation. However, the region in the parameter space, where large-scale dynamo action is observed, is small.  相似文献   

7.
Parker’s two-dimensional (2D) dynamo model with an algebraic form of nonlinearity for the α-effect is considered. The model uses geostrophic distributions for the α-effect and differential rotation, which are derived from the three-dimensional (3D) convection models. The resulting configurations of the magnetic field in the liquid core are close to the solutions in Braginsky’s Z-model. The implications of the degree of geostrophy observed in the 3D dynamo models for the behavior of the mean magnetic field are explored. It is shown that the reduction in geostrophy leads to magnetic field reversals accompanied by the relative growth of the nondipole component of the field on the surface of the liquid core. The simulations with a random α-effect which causes turbulent pulsations are carried out. The approach is capable of producing realistic sequences of magnetic reversals.  相似文献   

8.
Mean-field theory describes magnetohydrodynamic processes leading to large-scale magnetic fields in various cosmic objects. In this study magnetoconvection and dynamo processes in a rotating spherical shell are considered. Mean fields are defined by azimuthal averaging. In the framework of mean-field theory, the coefficients which determine the traditional representation of the mean electromotive force, including derivatives of the mean magnetic field up to the first order, are crucial for analyzing and simulating dynamo action. Two methods are developed to extract mean-field coefficients from direct numerical simulations of the mentioned processes. While the first method does not use intrinsic approximations, the second one is based on the second-order correlation approximation. There is satisfying agreement of the results of both methods for sufficiently slow fluid motions. Both methods are applied to simulations of rotating magnetoconvection and a quasi-stationary geodynamo. The mean-field induction effects described by these coefficients, e.g., the α-effect, are highly anisotropic in both examples. An α2-mechanism is suggested along with a strong γ-effect operating outside the inner core tangent cylinder. The turbulent diffusivity exceeds the molecular one by at least one order of magnitude in the geodynamo example. With the aim to compare mean-field simulations with corresponding direct numerical simulations, a two-dimensional mean-field model involving all previously determined mean-field coefficients was constructed. Various tests with different sets of mean-field coefficients reveal their action and significance. In the magnetoconvection and geodynamo examples considered here, the match between direct numerical simulations and mean-field simulations is only satisfying if a large number of mean-field coefficients are involved. In the magnetoconvection example, the azimuthally averaged magnetic field resulting from the numerical simulation is in good agreement with its counterpart in the mean-field model. However, this match is not completely satisfactory in the geodynamo case anymore. Here the traditional representation of the mean electromotive force ignoring higher than first-order spatial derivatives of the mean magnetic field is no longer a good approximation.  相似文献   

9.
Flow and transport models in heterogeneous geological formations are usually large-scale with excessive computational complexity and uncertain characteristics. Uncertainty quantification for predicting subsurface flow and transport often entails utilizing a numerical Monte Carlo framework, which repeatedly simulates the model according to a random field parameter representing hydrogeological characteristics of the aquifer. The physical resolution (e.g. spatial grid resolution) for the simulation is customarily chosen based on recommendations in the literature, independent of the number of Monte Carlo realizations. This practice may lead to either excessive computational burden or inaccurate solutions. We develop an optimization-based methodology that considers the trade-off between the following conflicting objectives: time associated with computational costs, statistical convergence of the model prediction and physical errors corresponding to numerical grid resolution. Computational resources are allocated by considering the overall error based on a joint statistical–numerical analysis and optimizing the error model subject to a given computational constraint. The derived expression for the overall error explicitly takes into account the joint dependence between the discretization error of the physical space and the statistical error associated with Monte Carlo realizations. The performance of the framework is tested against computationally extensive simulations of flow and transport in spatially heterogeneous aquifers. Results show that modelers can achieve optimum physical and statistical resolutions while keeping a minimum error for a given computational time. The physical and statistical resolutions obtained through our analysis yield lower computational costs when compared to the results obtained with prevalent recommendations in the literature. Lastly, we highlight the significance of the geometrical characteristics of the contaminant source zone on the optimum physical and statistical resolutions.  相似文献   

10.
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   

11.
Abstract

Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However the nonlinearities included arc (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by cousidering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave be achieved. Moreover this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.  相似文献   

12.
In Kim et al. (Kim, E., Hughes, D.W. and Soward, A.M., “An investigation into high conductivity dynamo action driven by rotating convection”, Geophys. Astrophys. Fluid Dynam. 91, 303–332 ().) we investigated kinematic dynamo action driven by rapidly rotating convection in a cylindrical annulus. Here we extend this work to consider self-consistent nonlinear dynamo action in which the back-reaction of the Lorentz force on the flow is taken into account. In particular, we investigate, as a function of magnetic Prandtl number, the evolution of an initially weak magnetic field in two different types of convective flow – one chaotic and the other integrable. On saturation, the latter shows a systematic dependence on the magnetic Prandtl number whereas the former appears not to. In addition, we show how, in keeping with the findings of Cattaneo et al. (Cattaneo, F., Hughes, D.W. and Kim, E., “Suppression of chaos in a simplified nonlinear dynamo model”, Phys. Rev. Lett. 76, 2057–2060 ().), saturation of the growth of the magnetic field is brought about, for the originally chaotic flow, by a strong suppression of chaos.  相似文献   

13.
We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory.  相似文献   

14.
According to present-day ideas, nonlinear saturation of the astrophysical dynamo and, in particular, the solar dynamo, are based on the consideration of the magnetic helicity balance, to which the helicities of the large-scale magnetic field and small-scale field related to it contributed. We show that, in a mirrorasymmetric medium, the small-scale magnetic field generated by the small-scale dynamo also has a nonzero magnetic helicity, which also should be taken into account in the magnetic helicity balance.  相似文献   

15.
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   

16.
Bias correction methods are usually applied to climate model outputs before using these outputs for hydrological climate change impact studies. However, the use of a bias correction procedure is debatable, due to the lack of physical basis and the bias nonstationarity of climate model outputs between future and historical periods. The direct use of climate model outputs for impact studies has therefore been recommended in a few studies. This study investigates the possibility of using reanalysis‐driven regional climate model (RCM) outputs directly for hydrological modelling by comparing the performance of bias‐corrected and nonbias‐corrected climate simulations in hydrological simulations over 246 watersheds in the Province of Québec, Canada. When using RCM outputs directly, the hydrological model is specifically calibrated using RCM simulations. Two evaluation metrics (Nash–Sutcliffe efficiency [NSE] and transformed root mean square error [TRMSE]) and three hydrological indicators (mean, high, and low flows) are used as criteria for this comparison. Two reanalysis‐driven RCMs with resolutions of 45 km and 15 km are used to investigate the scale effect of climate model simulations and bias correction approaches on hydrology modelling. The results show that nonbias‐corrected simulations perform better than bias‐corrected simulations for the reproduction of the observed streamflows when using NSE and TRMSE as criteria. The nonbias‐corrected simulations are also better than or comparable with the bias‐corrected simulations in terms of reproducing the three hydrological indicators. These results imply that the raw RCM outputs driven by reanalysis can be used directly for hydrological modelling with a specific calibration of hydrological models using these datasets when gauged observations are scarce or unavailable. The nonbias‐corrected simulations (at a minimum) should be provided to end users, along with the bias‐corrected ones, especially for studying the uncertainty of hydrological climate change impacts. This is especially true when using an RCM with a high resolution, since the scale effect is observed when the RCM resolution increases from a 45‐km to a 15‐km scale.  相似文献   

17.
Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress—Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of thermal to magnetic diffusivity. Attention is focused on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection. The case of main interest is the layer confined between electrically-insulating no-slip walls, but the analysis is guided by a parallel study based on illustrative boundary conditions that are mathematically simpler.  相似文献   

18.
The question of which climate model bias correction methods and spatial scales for correction are optimal for both projecting future hydrological changes as well as removing initial model bias has so far received little attention. For 11 climate models (CMs), or GCM/RCM – Global/Regional Climate Model pairing, this paper analyses the relationship between complexity and robustness of three distribution‐based scaling (DBS) bias correction methods applied to daily precipitation at various spatial scales. Hydrological simulations are forced by CM inputs to assess the spatial uncertainty of groundwater head and stream discharge given the various DBS methods. A unique metric is devised, which allows for comparison of spatial variability in climate model bias and projected change in precipitation. It is found that the spatial variability in climate model bias is larger than in the climate change signals. The magnitude of spatial bias seen in precipitation inputs does not necessarily correspond to the magnitude of biases seen in hydrological outputs. Variables that integrate basin responses over time and space are more sensitive to mean spatial biases and less so on extremes. Hydrological simulations forced by the least parameterized DBS approach show the highest error in mean and maximum groundwater heads; however, the most highly parameterised DBS approach shows less robustness in future periods compared with the reference period it was trained in. For hydrological impacts studies, choice of bias correction method should depend on the spatial scale at which hydrological impacts variables are required and whether CM initial bias is spatially uniform or spatially varying. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

19.
By the example of the dynamo model in the rotating plane layer heated from below, the effects are examined that lead to the stabilization of an exponentially growing magnetic field in the magnetostrophic convection in passing from the kinematic dynamo mode to the nonlinear mode. The estimates of the energy redistribution in the spectrum are given, and the mechanisms of suppression of helicity are presented. Equalization of the field of velocity and the magnetic field is analyzed. The modes examined are close to those utilized in the up-to-date models of the planetary dynamo in the cores of planets.  相似文献   

20.
We investigate the dynamo underpinning of solar cycle precursor schemes based on direct or indirect measures of the solar surface magnetic field. We do so for various types of mean-field-like kinematic axisymmetric dynamo models, where amplitude fluctuations are driven by zero-mean stochastic forcing of the dynamo number controlling the strength of the poloidal source term. In all stochastically forced models considered, the surface poloidal magnetic field is found to have precursor value only if it feeds back into the dynamo loop, which suggests that accurate determination of the magnetic flux budget of the solar polar fields may hold the key to dynamo model-based cycle forecasting.  相似文献   

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