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1.
本文利用MHD二维不可压模式,研究了地球磁层顶边界区剪切流引起的Kelvin-Helmholtz（K-H）不稳定性问题,得到了一个新的非线性微分方程组.理论和数值分析表明:该问题的非线性演化对初值非常敏感,而且在雷诺数和磁雷诺数给定的条件下,Alfven马赫数（MA）对K-H不稳定性的非线性演化起决定性作用.这组方程蕴含几个吸引子,如不动点,极限环和奇异吸引子等,这体现了磁层顶非线性系统的复杂性.文中还发现背景磁场在磁层顶K-H不稳定性的非线性演化过程中起很重要的作用. 相似文献
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Nonlinear dynamics of level variations in the Caspian Sea 总被引：2，自引：0，他引：2
Caspian Sea level variations, which have several equilibrium states, are studied by the methods of the theory of nonlinear dynamic systems. Normal monthly values of sea level according to data collected at Makhachkala gauge from 1900 to 2000 are considered. The diagnostic characteristics of dynamic chaos are used to show that sea level variations have some properties of series with chaotic behavior. A model of level variations in the Caspian Sea, comprising a system of water balance equations for the sea basin, the dynamics of river runoff, and water balance of the sea itself, is proposed. Equation of a nonlinear oscillator is derived and shown to have solutions with chaotic regimes at some combinations of parameters. 相似文献
4.
We present a systematic analysis of the dynamical behavior introduced by fault zone heterogeneities, using a simple mass-spring model with velocity-weakening friction. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by clastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. Symmetry stabilizes the system and generates only cyclic behavior. For an asymmetric system where the frictional forces for the two blocks are not equal, the solutions exhibit chaotic behavior. The transition from stable cyclic behavior to chaos is characterized by the period-doubling route to chaos. Lyapunov exponents are computed to quantify the deterministic chaos and to locate the onset of the chaotic evolution in parameter space. In many examples of deterministic chaos, chaotic behavior of a low-order system implies chaos in similar higher order systems. Thus, our results provide substantial evidence that crustal deformation is an example of deterministic chaos. 相似文献
5.
Short-range prediction experiments of the Kuroshio path variabilities south of Japan 总被引：1，自引：0，他引：1
Assimilation and prediction experiments of the Kuroshio path variability south of Japan were conducted to investigate the
predictability of the Kuroshio path. The assimilation and prediction system is composed of an eddy-resolving model and a three-dimensional
variational analysis scheme with vertical coupled temperature–salinity empirical orthogonal function modes. The sea surface
height (SSH) variability and the variations of the Kuroshio path of the assimilation fields are in good agreement with those
observed. The results of the assimilation are then used as the initial conditions for 138 cases of 90-day prediction experiments
conducted from 1993 to 2004. The predictive limit of our system is assessed by the SSH anomaly in the assimilation field and
is found to be around 40–60 days, which is much longer than that of the persistence. The prediction results show good performance
in the transition stage from a straight to a meandering path. For example, a large meandering event that occurred in August
2004 is successfully predicted in a 2-month forecast. Two types of failure cases are investigated. One is a case where the
eastward propagation speed of the meander is faster than a real state. The dynamical response of the model to the assimilation
revealed that an initial shock, caused by the dynamically unbalanced initial condition, induces the fast eastward propagation
of the meander. The other case exhibits an unrealistic meander. In this case, a cold anomaly at an intermediate layer in the
initial condition grows rapidly and results in the unrealistic meander. This implies that the Kuroshio path south of Japan
has a chaotic nature. These facts revealed by the failure cases give us some insight for improving the predictive skill of
the Kuroshio path variability. 相似文献
6.
Abstract The annulus model considers convection between concentric cylinders with sloping endwalls. It is used as a simplified model of convection in a rapidly rotating sphere. Large azimuthal wavenumbers are preferred in this problem, and this has been exploited to develop an asymptotic approach to nonlinear convection in the annulus. The problem is further reduced because the Taylor-Proudman constraint simplifies the dependence in the direction of the rotation vector, so that a nonlinear system dependent only on the radial variable and time results. As Rayleigh number is increased a sequence of bifurcations is found, from steady solutions to periodic solutions and 2-tori, typically ending in chaotic behaviour. Both the magnetic (MHD convection) and non-magnetic problem has been considered, and in the non-magnetic case our bifurcation sequence can be compared with those found by previous two-dimensional numerical simulations. 相似文献
7.
Nonlinear ensemble prediction of chaotic daily rainfall 总被引：3，自引：0，他引：3
The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955–2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on the phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996–2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. 相似文献
8.
This paper presents a study of high Rayleigh number (up to 200 times supercritical) axisymmetrical convection in a spherical shell with an aspect ratio relevant for the Earth's lower mantle. Both bottom-heated and internal heated cases have been considered. Computations have been carried out for an infinite Prandtl number isoviscous fluid with free slip isothermal boundary conditions. The first part of the paper is devoted to the influence of the resolution on the accuracy of the numerical results. It is shown that the resolution strongly influences the onset of time dependence. Recent methods of non-linear physics have been used to prove that the time dependence and the chaotic behaviors of the solutions are real ones. From these results we can confirm that convection is chaotic, in this particular geometry, even for Rayleigh numbers 200 times critical. Aperiodic boundary layer instabilities are found to be incapable of breaking up the large-scale flow, owing to the shear of the global circulation. Spectral analysis of the power associated with the thermal anomalies shows that there is an upward cascade of energy, due to small-scale chaotic instabilities, from l = 2 to l = 4–6 at the bottom boundary, in agreement with new seismic observations at the core-mantle boundary [1–3]. 相似文献
9.
Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems. 相似文献
10.
Numerical simulations of complex earthquake cycles are conducted using a two-degree-of-freedom spring-block model with a rate- and state-friction law, which has been supported by laboratory experiments. The model consisted of two blocks coupled to each other and connected by elastic springs to a constant-velocity, moving driver. By widely and systematically varying the model parameters, various slip patterns were obtained, including the periodic recurrence of seismic and aseismic slip events, and several types of chaotic behaviour. The transition in the slip pattern from periodic to chaotic is examined using bifurcation diagrams. The model system exhibits typical period-doubling sequences for some parameter ranges, and attains chaotic motion. Simple relationships are found in iteration maps of the recurrence intervals of simulated earthquakes, suggesting that the simulated slip behaviour is deterministic chaos. Time evolutions of the cumulative slip distance in chaotic slip patterns are well approximated by a time-predictable model. In some cases, both seismic and aseismic slip events occur at a block, and aseismic slip events complicate the earthquake recurrence patterns. 相似文献
11.
Xingzhong Shi Richard T. McNider M. P. Singh David E. England Mark J. Friedman William M. Lapenta William B. Norris 《Pure and Applied Geophysics》2005,162(10):1811-1829
Previous studies of the stable atmospheric boundary layer using techniques of nonlinear dynamical systems (MCNIDER et al., 1995) have shown that the equations support multiple solutions in certain parameter spaces. When geostrophic speed is used as a bifurcation parameter, two stable equilibria are found—a warm solution corresponding to the high-wind regime where the surface layer of the atmosphere stays coupled to the outer layer, and a cold solution corresponding to the low-wind, decoupled case. Between the stable equilibria is an unstable region where multiple solutions exist. The bifurcation diagram is a classic S shape with the foldback region showing the multiple solutions. These studies were carried out using a simple two-layer model of the atmosphere with a fairly complete surface energy budget. This allowed the dynamical analysis to be carried out on a coupled set of four ordinary differential equations. The present paper extends this work by examining additional bifurcation parameters and, more importantly, analyzing a set of partial differential equations with full vertical dependence. Simple mathematical representations of classical problems in dynamical analysis often exhibit interesting behavior, such as multiple solutions, that is not retained in the behavior of more complete representations. In the present case the S-shaped bifurcation diagram remains with only slight variations from the two-layer model. For the parameter space in the foldback region, the evolution of the boundary layer may be dramatically affected by the initial conditions at sunset. An eigenvalue analysis carried out to determine whether the system might support pure limit-cycle behavior showed that purely complex eigenvalues are not found. Thus, any cyclic behavior is likely to be transient. 相似文献
12.
Analytic solutions play an important role in the testing of models evaluated by numerical methods. This paper presents a straight forward method for determining analytic solutions to multiple species contaminant transport problems in porous media. The method uses Fourier sine transforms (as opposed to Laplace transforms) to obtain the solution of Cho (1970, Can. J. Soil. Sci., 51: 339–350) in a simpler way. It provides a flexible approach to the introduction of new boundary and initial conditions within the model. New solutions are presented for constant and exponential initial contaminant profiles. 相似文献
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Abstract Numerical solutions are obtained by implicit multigrid solvers for initial-value problems in the rotating Shallow-Water Equations (SWE) with spatially complex initial conditions. Companion solutions are also obtained with the Shallow-Water Balance Equations (SWBE), both to determine the initial conditions for the SWE and to provide a comparison solution that lies entirely on the slow, advective manifold. We make use of a control parameter (here the Rossby number, R) to regulate the degree of slowness and balance. While there are measurable discrepancies between the evolving SWE and SWBE solutions for all R, there is a distinct, spatially local breakdown both of the slow manifold in the SWE solution and in the closeness of correspondence between the SWE and SWBE solutions. This critical value for breakdown is only slightly smaller than the R values at which, first, the SWE evolution becomes singular (i.e., the fluid depth vanishes), or second, a consistent initial condition for the SWBE cannot be defined. This breakdown is most clearly evident in a sudden increase in vertical velocity near the center of a strong, cyclonic vortex; its behavior is primarily associated with an enhanced dissipation rather than an initiation of gravity-wave propagation. The numerical performance of the multigrid solvers is satisfactory even in the difficult circumstances near solution breakdown or singularity. 相似文献
15.
Further analysis of energetic electron precipitation at the evening sector of magnetosphere is performed. In the framework of the quantitative model of cyclotron wave-particle interactions developed in the previous Pasmanik et al. paper, the case of finite spread over energies of initial energetic electron distribution is studied. The solution for distribution function of energetic electron is found. The energetic spectrum of trapped and precipitating electrons and whistler wave spectrum are analysed. 相似文献
16.
Numerical simulation of an unsaturated flow equation 总被引：1，自引：1，他引：0
A numerical model for an unsaturated flow problem by using the finite element method is established in order to simulate liquid
moisture flow In an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary
conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles.
However, nonoscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped
finite element method. Moreover, the kind of boundary condition is handled very well.
Project supported by the National Key Project of Fundamental Research ”Climate Dynamics and Climate Prediction Theory“ and
China Postdoctoral Science Foundation. 相似文献
17.
S. J. Hogan 《地震工程与结构动力学》1990,19(7):1057-1071
Recent mathematical advances in the study of the response of a rigid block to horizontal simple harmonic forcing conclude that (i) all types of subharmonic response are possible, (ii) several types can occur at one point in parameter space, (iii) exact expressions are available for stability boundaries in parameter space, (iv) asymmetric solutions exist just outside the upper boundaries of symmetric solutions, (v) period- and impact-doubling cascades occur as parameter values are varied even further outside the boundaries, (vi) aperiodic (or chaotic) responses are possible, (vii) periodic responses can occur which appear to violate West's formula and (viii) steady state responses of the forced system can be so large as to produce toppling of the block if the system were unforced. These results are used to explain and extend recent computational work. Also we find quantitative agreement between our theoretical work and some recent experimental work of Tso and Wong. 相似文献
18.
A. Wiin-nielsen 《地球物理与天体物理流体动力学》2013,107(1):295-311
Abstract The investigation is concerned with the impact of initial uncertainties on predictions. The problem can be solved exactly for sufficiently simple non-linear systems where an exact solution to the deterministic problem is known. In this paper we shall use the advective equation as an example. It is found that the behavior at large times of the system depends on the initial uncertainty and the nature of the probability density function. In applications it is normally necessary to introduce a closure approximation because exact analytical solutions are unknown. Such a closure scheme based on the neglect of third and higher moments will be used in the example and solutions from the closure scheme will be compared with the exact solutions. It is found that the asymptotic values of the uncertainty may be less than the initial uncertainty. 相似文献
19.
In this study, NSGA‐II is applied to multireservoir system optimization. Here, a four‐dimensional multireservoir system in the Han River basin was formulated. Two objective functions and three cases having different constraint conditions are used to achieve nondominated solutions. NSGA‐II effectively determines these solutions without being subject to any user‐defined penalty function, as it is applied to a multireservoir system optimization having a number of constraints (here, 246), multi‐objectives, and infeasible initial solutions. Most research by multi‐objective genetic algorithms only reveals a trade‐off in the objective function space present, and thus the decision maker must reanalyse this trade‐off relationship in order to obtain information on the decision variable. Contrastingly, this study suggests a method for identifying the best solutions among the nondominated ones by analysing the relation between objective function values and decision variables. Our conclusions demonstrated that NSGA‐II performs well in multireservoir system optimization having multi‐objectives. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
20.
Debra M. Hurwitz Sylvan M. Long Eric B. Grosfils 《Journal of Volcanology and Geothermal Research》2009
Eruptions fed from subsurface reservoirs commonly construct volcanic edifices at the surface, and the growth of an edifice will in turn modify the subsurface stress state that dictates the conditions under which subsequent rupture of the inflating reservoir can occur. We re-examine this problem using axisymmetric finite element models of ellipsoidal reservoirs beneath conical edifices, explicitly incorporating factors (e.g., full gravitational loading conditions, an elastic edifice instead of a surface load, reservoir pressures sufficient to induce tensile rupture) that compromise previous solutions to illustrate why variations in rupture behavior can occur. Relative to half-space model results, the presence of an edifice generally rotates rupture toward the crest of a spherical reservoir, with increasing flank slope (for an edifice of constant volume) and larger edifices (or greater reservoir scaled depths) normally serving to enhance this trend. When non-spherical reservoirs are considered, the presence of an edifice amplifies previously identified half-space failure characteristics, shifting rupture to the crest more rapidly for prolate reservoirs while forcing rupture closer to the midpoint of oblate reservoirs. Rupture is always observed to occur in the σt orientation, and depending on where initial failure occurs rupture favors the initial emplacement of either lateral sills, circumferential intrusions or vertically ascending dikes. Ultimately, integration of our numerical model results with other information, for instance the sequence of intrusion/eruption events observed at a given volcano, can provide useful new insight into how a volcano's subsurface magma plumbing system evolved. We demonstrate this process through application of our model to Summer Coon, a well-studied stratocone on Earth, and Ilithyia Mons, a large conical shield volcano on Venus. 相似文献