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1.
R. Kaiser 《地球物理与天体物理流体动力学》2013,107(1-2):125-135
Abstract Bayly (1993) introduced and investigated the equation (? t + v·▽-η ▽2)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action. 相似文献
2.
Abstract In order to gain a better understanding of the processes that may give rise to non-axisymmetric magnetic fields in galaxies, we have calculated field decay rates for models with a realistic galactic rotation curve and including the effects of a locally enhanced turbulent magnetic diffusivity within the disc. In all cases we have studied, the differential rotation increases the decay rate of non-axisymmetric modes, whereas axisymmetric ones are unaffected. A stronger magnetic diffusivity inside the disc does not lead to a significant preference for non-axisymmetric modes. Although Elsasser's antidynamo theorem has not yet been proved for the present case of a non-spherical distribution of the magnetic diffusivity, we do not find any evidence for the theorem not to be valid in general. 相似文献
3.
Abstract The Lortz dynamo with helical symmetry is re-examined. It is shown that by imposing appropriate boundary conditions the set of possible solutions can be broken down into various classes characterized by the behavior of the mean magnetic field. It is found that, as the cylindrical radius, s, tends to zero, <BΦ> ～ 0(sj), <Bz> ～ const + 0(sj?i), where j>5. It is proved that the azimuthal wavenumber associated with the j=5 class is necessarily equal to 2. The existence of at least one cylindrical surface inside which the dynamo is self-sustained is demonstrated. A new simple explicit solution is obtained. The topology the magnetic field is studied and three-dimensional pictures of the magnetic field lines are exhibited. Finally, a criterion for reversal of the magnetic field as a function of radius is ohtained and is applied to our solution. 相似文献
4.
We have selected 171 near-field records from 391 aftershock records of the Lulong, Hebei Province, earthquake in October 1982
and relocated the hypocenter of 45 aftershocks using the program Hypoinverse. The distribution of aftershocks reveals a set
of earthquake faults: a WNW stretching fault truncates two NNE stretching faults. The two branches of faults show the conjugate
structure which is often seen in brittle fracture. The NNE stretching faults are connected together. The Luanhe river valley
near Lulong developed to a rudiment rift basin surrounded by a series of faults. The fault of Lulong earthquake is a strike-slip
fault with tension component. This fault type matches with the activity of Zhangjiakou-Bohai seismic belt (Zhang-Bo belt)
and also shows the action of Zhang-Bo belt as a boundary of two secondary active blocks that truncates the NNE fault.
Foundation item: National Natural Science Foundation of China (40234038).
Contribution No. 05FE3016, Institute of Geophysics, China Earthquake Administration. 相似文献
5.
Toshihiro Sakamoto 《地球物理与天体物理流体动力学》2013,107(3):179-199
It is shown that the deep western boundary current (DWBC) in the North Atlantic may contribute to premature separation of the Gulf Stream. A simple analytical study is made based on the linear barotropic vorticity equation in which a possible effect of the DWBC is introduced as anomalous stretching of the water column in a manner consistent with certain qualitative aspects of the observed features. This additional positive vorticity may be generated by a deep downwelling associated with horizontal shears of the DWBC. It is found that separation latitudes are farther to the south as the stretching is strengthened. Vertical motion required for a southward shift of order unity (e.g., 500 km) is estimated to be of the order of 0.05 mm s m 1 , in reasonable agreement with the observed values. It is suggested that since the DWBC is intimately linked with the thermohaline circulation, a meridional migration of the Gulf Stream separation might reflect long-term variations in the North Atlantic. 相似文献
6.
Abstract Three approaches to modelling the duration of streamflow droughts at eight southern African sites are considered; a non-parametric method (that of Kaplan-Meier) is compared with the fitting of two simple parametric models: the exponential and Weibull. All techniques allow the instantaneous probability of a drought coming to an end to differ between wet and dry seasons, using the concept of censored data. Model-fitting is discussed, and the Kaplan-Meier estimates permit an assessment of the fit of the parametric models, with the aim of finding a parsimonious model for the data, which can be used for predictive purposes. In most cases considered herein, either the exponential or Weibull approach is found to be adequate. 相似文献
7.
Abstract In this paper we study the stability of an idealised magnetostatic coronal loop, incorporating both the effect of line-tying, due to the dense photosphere, and of pressure gradients. The stability equations may be solved analytically for our particular equilibrium. From the marginally stable case, the critical conditions separating instability from stability are derived. It is found that stretching or twisting a loop eventually makes it kink unstable. 相似文献
8.
Yu Zhong Yonghong Hao Xueli Huo Mingkun Zhang Qingyun Duan Yonghui Fan 《水文科学杂志》2013,58(11):2011-2023
ABSTRACTTo acquire better understanding of spring discharge under extreme climate change and extensive groundwater pumping, this study proposed an extreme value statistical decomposition model, in which the spring discharge was decomposed into three items: a long-term trend; periodic variation; and random fluctuation. The long-term trend was fitted by an exponential function, and the periodic variation was fitted by an exponential function whose index was the sum of two sine functions. A general extreme value (GEV) model was used to obtain the return level of extreme random fluctuation. Parameters of the non-linear long-term trend and periodic variation were estimated by the Levenberg-Marquardt algorithm, and the GEV model was estimated by the maximum likelihood method. The extreme value statistical decomposition model was applied to Niangziguan Springs, China to forecast spring discharge. We showed that the modelled spring discharge fitted the observed data very well. Niangziguan Springs discharge is likely to continue declining with fluctuation, and the risk of cessation by August 2046 is 1%. The extreme value decomposition model is a robust method for analysing the nonstationary karst spring discharge under conditions of extensive groundwater development/pumping, and extreme climate changes.
Editor D. Koutsoyiannis; Associate editor J. Ward 相似文献
9.
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
10.
AbstractThe standardized series of monthly and weekly flow sequences, referred to as standardized hydrological index (SHI) series, from five rivers in the Canadian prairies were subjected to return period (Tr) analysis of drought length (L). The SHI series were truncated at drought probability levels q ranging from 0.5 to 0.05 with the intention of deducing drought events and corresponding drought lengths. The values of L were fitted to the Pearson 3, the gamma (2-parameter), the exponential (1-parameter), the Weibull 3 and the Weibull (2-parameter) probability density functions (pdfs). A priori assignment of one week or one month for the location parameter in the Pearson 3 pdf proved logical and also facilitated the rapid estimation of other parameters using either the method of moments or the method of maximum likelihood. The Pearson 3 turns out to be the most suitable pdf to describe and to estimate return periods of drought lengths. At the monthly and weekly time scales, it was inferred that the sample size (T, months or weeks) of SHI series could be treated equivalent to the return period of the largest recorded drought length. At the annual time scale, however, the sample size (T, years) should be modified using either the Hazen or the Gringorten plotting position formula to reflect the actual return period of the largest recorded drought length in years.
Editor D. Koutsoyiannis; Associate editor E. Gargouri 相似文献
11.
ABSTRACTThe modelling of soil loss and investigation of urban hydrology and wet weather pollution in Malaysia requires the definition of rainfall parameters for the region. In this study, an inexpensive method was applied to establish the influence of raindrop diameter on kinetics and rain intensity in Skudai, Peninsular Malaysia, as a prelude to wider regional research. Raindrop sizes vary from less than 1.2 mm to as big as 7.0 mm, with median raindrop diameters of 2.51 mm and a mean diameter of 2.56 mm. The median raindrop diameter–intensity relationship correlates strongly using power and exponential equations, with coefficients of determination of 0.75 and 0.73, respectively. The kinetic energy–intensity relationship fits an exponential function and also a linear equation with R2 values of 0.49 and 0.34, respectively. An average rain kinetic energy of 30 J m-2 mm-1 was recorded. This research leads to an objective reclassification of rainfall intensities in the region.
Editor Z.W. Kundzewicz; Associate editor not assigned 相似文献
12.
Abstract Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2. 相似文献
13.
The present study demonstrates how the Paleo-Proterozoic Wangtu Gneissic Complex (WGC) of the Lesser Himalayan Crystalline sequence experienced superposed folding and doming prior to its exhumation, with the help of integrated field, microstructural, magnetic fabric anisotropy and geochronological studies. The WGC forms the basement of the Lesser Himalaya and is bounded by Vaikrita Thrust (VT) to the northeast and Munsiari Thrust (MT) to the southwest. The regional structure consists of upright large scale early folds (D1) trending NW–SE. The mesoscopic fabric is related to axial plane foliation of the D1 folds and, to a lesser extent, late D2 folds. The axis of maximum compression for D1 and D2 folds are mutually orthogonal. The D1 folds have formed simultaneously with the major Himalayan thrusts whereas the D2 folds have developed during a later deformation event. The magnetic lineation at the hangingwall of the VT is sub-horizontal indicating stretching along the strike of the thrust. In the interior parts of the WGC, the magnetic fabric is of two types: (i) magnetic lineation demarks the intersection of mesoscopic and magnetic foliation indicating superposed deformation and (ii) scattered distribution of magnetic lineations due to D2 folding on initially curved and non-cylindrical D1 surface. 40Ar–39Ar dating of biotite from one site from the core of WGC gives an age of 9.3 ± 0.3 (2σ) Ma. It is inferred that the doming of the WGC took place at ∼9 Ma and, instead of large scale thrusting, it is characterized by superposed folding and strike-parallel stretching along the VT zone. It is suggested that the effect of superposed folding and ductile deformation of the Himalayan basement rocks has to be taken into account before cross-section balancing or any estimation of crustal shortening is attempted. 相似文献
14.
Raymond Hide 《地球物理与天体物理流体动力学》2013,107(1-3):69-79
Abstract ‘‘Helicity'’ density H ≡ u · ω and other pseudo-scalar fields such as P ≡ ω · Vlnρ (which is related to Ertel potential vorticity) are useful quantities in theoretical fluid dynamics and magneto-fluid dynamics. Here u denotes the Eulerian flow velocity relative to the chosen frame of reference, ω ≡ V × u is the corresponding relative vorticity and ρ the mass density of the fluid. A general expression is readily obtained for ?H/?t (where t denotes time) in terms of P and the ‘‘superhelicity'’ density S ≡ ω · V × ω which, in fluids of low viscosity, has its highest values in boundary layers. One need for such a relationship became evident during an attempt to interpret the findings of laboratory experiments on thermal convection in rotating fluids in containers of various geometrical shapes and topological characteristics. In electrodynamics an analogous expression can be found relating the time rate of change of ‘‘magnetic helicity'’ A · B to ‘‘magnetic superhelicity'’ B · ? × B (where B · ? × A is the magnetic field) and a scalar quantity analogous to P which involves non-Ohmic contributions to the relationship between the electric current density and the electric field. 相似文献
15.
The generation of magnetic fields in space plasmas and in astrophysics is usually described within the framework of magnetohydrodynamics. Turbulent helical flows produce magnetic fields very efficiently, with correlation length scales larger than those characterizing the flow. Within the context of the solar magnetic cycle, a turbulent dynamo is responsible for the so-called alpha effect, while the Omega effect is associated to the differential rotation of the Sun.We present direct numerical simulations of turbulent magnetohydrodynamic dynamos including two-fluid effects such as the Hall current. More specifically, we study the evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence, and explore the conditions for exponential growth of the magnetic energy. In all the cases considered, we find that the dynamo saturates at the equipartition level between kinetic and magnetic energy, and the total energy reaches a Kolmogorov power spectrum. 相似文献
16.
John V. Shebalin 《地球物理与天体物理流体动力学》2013,107(4):411-466
Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B o?=?0 and weakly broken when B o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects. 相似文献
17.
O.M. Podvigina 《地球物理与天体物理流体动力学》2013,107(2):149-174
We are investigating numerically the nonlinear behaviour of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small enough for the trivial solution with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non-vanishing magnetic field appear in this bifurcation. Subsequent bifurcations are investigated. A regime is detected, where chaotic variations of the magnetic field orientation (analogous to magnetic field reversals) are observed in the temporal evolution of the system. 相似文献
18.
Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry. 相似文献
19.
ABSTRACTIn this study we analyzed two models commonly used in remote sensing-based root-zone soil moisture (SM) estimations: one utilizing the exponential decaying function and the other derived from the principle of maximum entropy (POME). We used both models to deduce root-zone (0–100 cm) SM conditions at 11 sites located in the southeastern USA for the period 2012–2017 and evaluated the strengths and weaknesses of each approach against ground observations. The results indicate that, temporally, at shallow depths (10 cm), both models performed similarly, with correlation coefficients (r) of 0.89 (POME) and 0.88 (exponential). However, with increasing depths, the models start to deviate: at 50 cm the POME resulted in r of 0.93 while the exponential filter (EF) model had r of 0.58. Similar trends were observed for unbiased root mean square error (ubRMSE) and bias. Vertical profile analysis suggests that, overall, the POME model had nearly 30% less ubRMSE compared to the EF model, indicating that the POME model was relatively better able to distribute the moisture content through the soil column. 相似文献
20.
The effect of the mutual orientation of the Poynting vector P of the electromagnetic energy density in the solar wind and the vector M of the Earth’s magnetic moment (taking into account its orbital and diurnal motions) on the geomagnetic activity has been
examined for the first time using the measurements of the solar wind parameters on the Earth orbit in 1963–2005. The component
P
m of the vector P along the vector M is shown to have a pronounced annual variation with the extrema in November and May and a diurnal variation with the extrema
at ∼6 and 18 UT. The phases of the variations are shown to be determined only by the geometric parameters and are independent
of the sign of the sector structure of the interplanetary magnetic field. The experimental data on the planetary and high-latitude
geomagnetic activity, which is a response to changes in the orientation of P relative to M, are presented. The power of the sources of the electromagnetic energy of the solar wind during strong geomagnetic disturbances
is also estimated. 相似文献