共查询到20条相似文献，搜索用时 15 毫秒
1.
Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed
by the first author recently, is obtained by numerical approach for the two-dimensional quasigeostrophic model in this paper.
The difference between the linear and nonlinear fastest growing perturbations is demonstrated. Moreover, local nonlinear fastest
growing perturbations are also found numerically. This is one of the essential differences between linear and nonlinear theories,
since in former case there is no local fastest growing perturbation. The results show that the nonlinear local fastest growing
perturbations play a more important role in the study of the first kind of predictability than the nonlinear global fastest
growing perturbation. 相似文献
2.
V. A. Zheligovsky 《Izvestiya Physics of the Solid Earth》2006,42(12):1051-1067
The problem of weakly nonlinear stability with respect to large-scale perturbations in 3-D convective magnetohydrodynamic (MHD) states in which the α-effect is absent or insignificant (e.g., because the system has symmetry relative to a center or a vertical axis) is examined. It is assumed that the MHD state whose stability is studied is free from large spatiotemporal scales and is insensitive to perturbations with the same small spatial scale as in the state under study. The equations for mean perturbation fields derived by asymptotic methods generalize the standard equations of magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). A combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms similar to advective terms arise in the inferred generalized equations. 相似文献
3.
A. B. Druzhinin 《Pure and Applied Geophysics》1996,148(3-4):637-683
A comprehensive approach, based on the general nonlinear ray perturbation theory (Druzhinin, 1991), is proposed for both a fast and accurate uniform asymptotic solution of forward and inverse kinematic problems in anisotropic media. It has been developed to modify the standard ray linearization procedures when they become inconsistent, by providing a predictable truncation error of ray perturbation series. The theoretical background consists in a set of recurrent expressions for the perturbations of all orders for calculating approximately the body wave phase and group velocities, polarization, travel times, ray trajectories, paraxial rays and also the slowness vectors or reflected/transmitted waves in terms of elastic tensor perturbations. We assume that any elastic medium can be used as an unperturbed medium. A total 2-D numerical testing of these expressions has been established within the transverse isotropy to verify the accuracy and convergence of perturbation series when the elastic constants are perturbed. Seismological applications to determine crack-induced anisotropy parameters on VSP travel times for the different wave types in homogeneous and horizontally layered, transversally isotropic and orthorhombic structures are also presented. A number of numerical tests shows that this method is in general stable with respect to the choice of the reference model and the errors in the input data. A proof of uniqueness is provided by an interactive analysis of the sensitivity functions, which are also used for choosing optimum source/receiver locations. Finally, software has been developed for a desktop computer and applied to interpreting specific real VSP observations as well as explaining the results of physical modelling for a 3-D crack model with the estimation of crack parameters. 相似文献
4.
G.D. Aburjania Kh.Z. Chargazia O.A. Kharshiladze 《Journal of Atmospheric and Solar》2010,72(13):971-981
The generation and further linear and nonlinear dynamics of planetary ultra-low-frequency (ULF) waves are investigated in the rotating dissipative ionosphere in the presence of inhomogeneous zonal wind (shear flow). Planetary ULF magnetized Rossby type waves appear as a result of interaction of the medium with the spatially inhomogeneous geomagnetic field. An effective linear mechanism responsible for the intensification and mutual transformation of large scale magnetized Rossby type and small scale inertial waves is found. For shear flows, the operators of the linear problem are not self-conjugate, and therefore the eigenfunctions of the problem may not be orthogonal and can hardly be studied by the canonical modal approach. Hence, it becomes necessary to use the so-called nonmodal mathematical analysis. The nonmodal analysis shows that the transformation of wave disturbances in shear flows is due to the non-orthogonality of eigenfunctions of the problem in the conditions of linear dynamics. Using numerical modeling, the peculiar features of the interaction of waves with the background flow as well as the mutual transformation of wave disturbances are illustrated in the ionosphere. It has been shown that the shear flow driven wave perturbations effectively extract an energy of the shear flow increasing the own energy and amplitude. These perturbations undergo self-organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation’s front. Depending on the features of the velocity profiles of the shear flows the nonlinear vortex structures can be either monopole vortices or vortex streets and vortex chains. 相似文献
5.
6.
从包含完整Coriolis力的Boussinesq近似的斜压大气运动方程组出发,利用半地转近似导出β效应和地球旋转水平分量fH=2Ωcosφ共同作用下的大气非线性Rossby波动所满足的KdV方程,求得了椭圆余弦波解和孤立波解.结果分析表明,若扰动与纬度有关,Coriolis参数分量fH将影响波动传播的频率特征,并加强水平散度对斜压Rossby波的作用;如果扰动与纬度无关,则 Coriolis 参数分量fH的影响消失. 相似文献
7.
H. L. Kuo 《Pure and Applied Geophysics》1972,96(1):171-175
Summary It is shown that the general nonlinear potential vorticity equation for viscous and conductive fluid in a rotating system can be expressed in terms of the geostrophic stream function for the horizontal velocity alone, provided that the motions are hydrostatic and quasi-geostrophic and the Richardson number is much larger than unity. The form of this equation is identical with that obtained from an asymptotic expansion for a small Rossby number. 相似文献
8.
V. A. Zheligovsky 《Izvestiya Physics of the Solid Earth》2006,42(3):244-253
The problem of weakly nonlinear stability of 3-D centrally symmetric magnetohydrodynamic systems to perturbations involving large scales is considered. It is assumed that large space-time scales are absent in the magnetohydrodynamic state under study, which is stable with respect to perturbations whose scales are as small as those of the state itself. Equations derived by asymptotic methods for average fields of perturbations generalize the Navier-Stokes and magnetic induction equations. They include a combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms. An effective method is proposed for the calculation of coefficients of eddy diffusion and advection in equations governing average fields. 相似文献
9.
10.
11.
Introduction The fluid outer core separates the solid inner core from the solid elastic mantle, and as a result, makes the free and forced movement of this mechanical system more complicated and profuse. As the elastic mantle, the free oscillations may occur within the Earths fluid outer core (FOC) due to excitation of a strong and deep earthquake (Crossley, 1975b; Friedlander, Siegmann, 1982; Shen, 1983; Friedlander, 1985). However, compared with the oscillations of the elastic mantle, i… 相似文献
12.
A stochastic approach to nonlinear unconfined flow subject to multiple random fields 总被引：3，自引：3，他引：0
Liangsheng Shi Jinzhong Yang Dongxiao Zhang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(6):823-835
In this study, the KLME approach, a moment-equation approach based on the Karhunen–Loeve decomposition developed by Zhang
and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random fields with known means and covariance functions. The F, R, H and Q are first decomposed into finite series in terms of Gaussian standard random variables by the Karhunen–Loeve expansion. The
hydraulic head h is then represented by a perturbation expansion, and each term in the perturbation expansion is written as the products of
unknown coefficients and Gaussian standard random variables obtained from the Karhunen–Loeve expansions. A series of deterministic
partial differential equations are derived from the stochastic partial differential equations. The resulting equations for
uncorrelated and perfectly correlated cases are developed. The equations can be solved sequentially from low to high order
by the finite element method. We examine the accuracy of the KLME approach for the groundwater flow subject to uncorrelated
or perfectly correlated random inputs and study the capability of the KLME method for predicting the head variance in the
presence of various spatially variable parameters. It is shown that the proposed numerical model gives accurate results at
a much smaller computational cost than the Monte Carlo simulation. 相似文献
13.
An analytical modelling framework is proposed to reproduce the frequently observed but poorly studied occurrence of mid‐channel bars in meandering channels. Mid‐channel bars occur in meanders and may characterize transitional morphologies between pure meandering and braided rivers. Based on existing field and experimental observations, we propose that two different mechanisms can generate central topographical patterns in meanders. A former mechanism (‘width‐forced’) is related to spatial width oscillations which determine a laterally symmetrical bed shear stress pattern that promotes mid‐channel bars. A second mechanism (‘curvature‐forced’) can take place also in curvilinear equiwidth streams since also longitudinal variations of channel curvature can produce laterally symmetrical alterations of the sediment transport capacity. A perturbation approach is employed to model both mechanisms within a common framework, allowing reproduction, at least qualitatively, of several observed features. While width‐forced mid‐channel bars are a symmetric linear altimetric response, to reproduce curvature‐forced mid‐channel bars requires modelling nonlinear flow‐bed topography interactions at the second order of the perturbation expansion. Hypotheses on how these mechanisms operate are further discussed through an application to field cases. The amplitude of the nonlinear response can be relevant compared to that of the point bar in equiwidth meanders and the location of mid‐channel bars seldom coincides with bend apexes, mainly depending upon the intrinsic meander wavelength. Central bars tend to symmetrically divert the flow against the two banks, a process which is proposed as a possible cause of cross‐sectional overwidening, along with the asymmetry between the rates of bank erosion and of the opposite bank accretion. The outcomes of this first modelling step on the subject allow discussion of the mutual feedback processes that characterize interactions between mid‐channel bars and width variations in river meanders. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
14.
《Advances in water resources》1998,21(7):581-590
Advances in computer power and in reservoir characterization allow simulation of pressure transients in complex reservoirs generated stochastically. Generally, interpretation of these transient gives useful information about the reservoir hydraulic properties: a major goal is to interpret these transients in the stochastic context. First we ensemble average the pressure over all the random permeability field realizations to derive an equation which drives the ensemble averaged pressure. We use the Fourier transform in space and the Laplace transform in time, in conjuction with a perturbation series expansion in successive powers of the permeability fluctuations to obtain an explicit solution. The Nth order term of this series involves the hydrodynamic interaction between N permeability heterogeneities and after averaging we obtain an expansion containing correlation functions of permeability fluctuations of increasing order.Next, Feynman graphs are introduced allowing a more attractive graphical interpretation of the perturbation series. Then series summation techniques are employed to reduce the graph number to be summed at each order of the fluctuation expansion. This in turn gives useful physical insights on the homogenization processes involved. In particular, it is shown that the sum of the so-called ‘one-particle irreducible graphs’ gives the kernel of a linear integro-differential equation obeyed by the ensemble average pressure. All the information about the heterogeneity structure is contained in this renormalized kernel, which is a limited range function.This equation on its own is the starting point of useful asymptotic results and approximations. In particular it is shown that interpretation of pumping tests yields the steady-state equivalent permeability after a sufficiently long time for an infinite reservoir, as expected. 相似文献
15.
Przemysław Figura 《地球物理与天体物理流体动力学》2017,111(6):508-526
We examine the equations that are used to describe flows which preserve field lines. We study what happens if we introduce perturbations to the governing equations. The stability of the line preserving flows in the case of the magneto-fluids permeated by magnetic fields is strictly connected to the non-null magnetic reconnection processes. In most of our study we use the Euler potential representation of the external magnetic field. We provide general expressions for the perturbations of the Euler potentials that describe the magnetic field. Similarly, we provide expressions for the case of steady flow as well as we obtain certain conditions required for the stability of the flow. In addition, for steady flows we formulate conditions under which the perturbations of the external field are negligible and the field may be described by its initial unperturbed form. Then we consider the flow equation that transforms quantities from the laboratory coordinate system to the related external field coordinate system. We introduce perturbations to the equation and obtain its simplified versions for the case of a steady flow. For a given system, use of this method allows us to simplify the considerations provided that some part of the system may be described as a perturbation. Next, to study regions favourable for the magnetic reconnection to occur we introduce a deviation vector to the basic line preserving flows condition equation. We provide expressions of the vector for some simplifying cases. This method allows us to examine if given perturbations either stabilise the system or induce magnetic reconnection. To illustrate some of our results we study two examples, namely a simple laboratory plasma flow and a simple planetary magnetosphere model. 相似文献
16.
Andrea Cortis Carlos E. Puente Bellie Sivakumar 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(7):897-906
We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of patterns encountered
in environmental applications. The procedure, which is based on transformations of multifractal distributions via fractal
functions, is extended through the introduction of nonlinear perturbations in the generating iterated linear maps. We demonstrate,
by means of various simulations based on changes in parameters, that the nonlinear perturbations generate yet a richer collection
of interesting patterns, as reflected by their overall shapes and their statistical and multifractal properties. It is shown
that the nonlinear extensions yield structures that closely resemble complex hydrologic spatio-temporal datasets, such as
rainfall and runoff time series, and width-functions of river networks. The implications of this nonlinear approach for environmental
modeling and prediction are discussed. 相似文献
17.
G. Christakos C. T. Miller D. Oliver 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(3):213-239
As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations. 相似文献
18.
A bridge is highlighted between the direct inversion and the indirect inversion. They are based on fundamental different approaches: one is looking after a projection from the data space to the model space while the other one is reducing a misfit between observed data and synthetic data obtained from a given model. However, it is possible to obtain similar structures for model perturbation, and we shall focus on P-wave velocity reconstruction. This bridge is built up through the Born approximation linearizing the forward problem with respect to model perturbation and through asymptotic approximations of the Green functions of the wave propagation equation. We first describe the direct inversion and its ingredients and then we focus on a specific misfit function design leading to a indirect inversion. Finally, we shall compare this indirect inversion with more standard least-squares inversion as the FWI, enabling the focus on small weak velocity perturbations on one side and the speed-up of the velocity perturbation reconstruction on the other side. This bridge has been proposed by the group led by Raul Madariaga in the early nineties, emphasizing his leading role in efficient imaging workflows for seismic velocity reconstruction, a drastic requirement at that time. 相似文献
19.
A.N. Belyaev 《Journal of Atmospheric and Solar》2009,71(17-18):1974-1981
A three-dimensional model is used to investigate the relations between parameters of atmospheric gravity waves (GW) and the spatial structure of O2 atmospheric (0,0) nightglow wave perturbations observed from space. It is shown that observed perturbations may be divided into the linear and nonlinear parts. The linear perturbations appear as wavelet signatures observed at certain viewing directions. The nonlinear part of the perturbations causes an increase in all sky brightness of the O2 atmospheric (0,0) nightglow. The model shows that at certain viewing directions the cancellation effect for waves passing through the emission layer disappears. The latter gives the opportunity to create the complete set of functions that may be used for the spectral decomposition of observed brightness field. The obtained spectrum may be interpreted in terms of the Fourier coefficients of 3D-decomposition of the temperature fluctuations induced by gravity waves just near the emission layer. 相似文献
20.
Lake Tana is the largest fresh water body situated in the north‐western highlands of Ethiopia. In addition to its ecological services, it serves for local transport, electric power generation, fishing, recreational purposes, and source of dry season irrigation water supply. Evidence shows that the lake has dried at least once at about 15,000–17,000 before present owing to a combination of high evaporation and low precipitation events. Past attempts to understand and simulate historical fluctuation of Lake Tana based on simplistic water balance approach of inflow, outflow, and storage have failed to capture well‐known events of drawdown and rise of the lake that have happened in the last 44 years. This study tested different stochastic methods of lake level and volume simulation for supporting Lake Tana operational planning decision support. Three stochastic methods (perturbations approach, Monte Carlo methods, and wavelet analysis) were employed for lake level and volume simulation, and the results were compared with the stage level measurements. Forty‐four years of daily, monthly, and mean annual lake level data have shown a Gaussian variation with goodness of fit at 0.01 significant levels of the Kolmogorov–Smirnov test. The stochastic simulations predicted the lake stage level of the 1972, 1984, and 2002/2003 historical droughts 99% of the time. The information content (frequency) of fluctuation of Lake Tana for various periods was resolved using Wigner's Time‐Frequency Decomposition method. The wavelet analysis agreed with the perturbations and Monte Carlo simulations resolving the time (1970s, 1980s, and 2000s) in which low frequency and high spectral power fluctuation has occurred. The Monte Carlo method has shown its superiority for risk analysis over perturbation and deterministic method whereas wavelet analysis reconstructed historical record of lake stage level at daily and monthly time scales. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献