Linear theory of rotating fluids using spherical harmonics part I: Steady flows     

Michel Rieutord 《地球物理与天体物理流体动力学》2013,107(3):163-182

Abstract

It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids.

These solutions are regular throughout the whole domain of the fluid and are not much affected by the equatorial singularity of steady boundary layers in spherical geometries.

A comparison between this method and the one based on boundary layer theory is carried out in the case of the steady spin-up of a fluid inside a sphere.  相似文献   

Three‐dimensional time‐harmonic fundamental solutions for a fluid‐saturated poroelastic half‐space with partially permeable free surface          下载免费PDF全文

Ahmad Pooladi  Mohammad Rahimian  Ronald Y. S. Pak 《国际地质力学数值与分析法杂志》2016,40(14):1903-1935

By virtue of a pair of scalar potentials for the displacement of the solid skeleton and the pore fluid pressure field of a saturated poroelastic medium, an alternative solution method to the Helmholtz decomposition is developed for the wave propagation problems in the framework of Biot's theory. As an application, a comprehensive solution for three‐dimensional response of an isotropic poroelastic half‐space with a partially permeable hydraulic free surface under an arbitrarily distributed time‐harmonic internal force field and fluid sources is developed. The Green's functions for the poroelastic fields, corresponding to point, ring, and disk loads, are reduced to semi‐infinite complex‐valued integrals that can be evaluated numerically by an appropriate quadrature scheme. Analytical and numerical comparisons are made with existing elastic and poroelastic solutions to illustrate the quality and features of the solution. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell     

Zi-Ping Sun  Gerald Schubert  Gary A. Glatzmaier 《地球物理与天体物理流体动力学》2013,107(1-4):95-131

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor number T _a =10⁶ and Prandtl number Pr=1 and with increasing Rayleigh number R, convection undergoes a series of bifurcations from onset of steadily propagating motions SP at R=R _c = 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained at R = 1.3R _c , R = 1.7 R _c , R = 2R _c , and R = 5 R _c , respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave number m of the convection pattern oscillates among m = 3,4,5, and 6; the convection pattern near the outer shell has larger m than that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts in m for the NP state at R = 5R _c , whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained at R = 50R _c . At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases except R = 50R _c , at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.  相似文献   

Application of the exact constitutive relationship of modified Cam clay to the undrained expansion of a spherical cavity     

Vincenzo Silvestri  Ghassan Abou‐Samra 《国际地质力学数值与分析法杂志》2011,35(1):53-66

The modified Cam clay (MCC) model is used to study the response of virgin‐compressed clay subjected to undrained triaxial compression. The MCC constitutive relationship is obtained in a closed form. Both elastic and plastic deviatoric strains are considered in the analysis. The solution allows to obtain total and effective stress paths followed by the clay in undrained spherical expansion. Pore water pressures are determined from the difference between total and effective mean stresses. For illustration purposes, the analysis is also applied to the well‐known reconstituted normally consolidated London clay and the results are compared with the recently published data obtained by a numerical approach. In addition, the Almansi large strains are used in the analysis, as these allow to obtain limit expansion and pore pressures, whereas both small‐strain and logarithmic‐strain approaches do not permit to determine them. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

局部凸线性拓扑空间Kannan型非扩张集值映射不动点定理     

林强 《广东海洋大学学报》2007,27(4):67-70

在Hausdorff局部凸线性拓扑空间中得到了Kannan型非扩张集值映射不动点定理,附带给出单值映射族具有公共不动点的结果。  相似文献   

全球强震的分布及其与地球自转速率变化的关系   总被引：4，自引：0，他引：4  

马利华  韩延本  尹志强 《天文研究与技术》2007,4(4):406-411

结合文[1]作者给出的全球地震目录,重点考察1832~1994年间全球强震(Ms≥7.5)的分布特征,并初步探讨了全球强震与地球自转速率变化的可能关联。结果表明,1832年以来的全球强震分布与现代的地震观测结果比较一致,这些强震主要集中在环太平洋和地中海—喜马拉雅两大地震带,地球自转速率变化与全球强震的频次存在较为密切的联系。  相似文献   

Ecogeomorphic state variables and phase‐space construction for quantifying the evolution of vegetated aeolian landscapes     

Andreas C. W. Baas  Joanna M. Nield 《地球表面变化过程与地形》2010,35(6):717-731

Cellular automaton modelling for the simulation of dune field formation and evolution has developed progressively in aeolian geomorphology in the last decade or so. A model that incorporates the effects of vegetation and its interactions with geomorphic landscape development – the Discrete Ecogeomorphic Aeolian Landscapes (DECAL) model – can replicate a number of important visual and qualitative aspects of the complex evolution of aeolian dune landscapes under the influence of vegetation dynamics in coastal environments. A key challenge in this research area is the analysis and comparison of both simulated and real‐world vegetated dune landscapes using objective and quantifiable principles. This study presents a methodological framework or protocol for numerically quantifying various ecogeomorphic attributes, using a suite of mathematically defined landscape metrics, to provide a rigorous and statistical evaluation of vegetated dune field evolution. Within this framework the model parameter space can be systematically explored and simulation outcomes can be methodically compared against real‐world landscapes. Based on a simplified scenario of parabolic dunes developing out of blow‐outs the resulting dune field realizations are investigated as a function of variable growth vigour of two simulated vegetation types (pioneer grass and successional woody shrub) by establishing a typological phase‐diagram of different landscape classes. The set of simulation outcomes furthermore defines a higher‐dimensional phase‐space, whose axes or dimensions can be interpreted by analysing how individual ecogeomorphic landscape metrics, or state variables, contribute to the data distribution. Principal component analysis can reduce this to a visual three‐dimensional (3D) phase‐space where landscape evolution can be plotted as time‐trajectories and where we can investigate the effects of changing environmental conditions partway through a simulation scenario. The use of landscape state variables and the construction of a 3D phase‐space presented here may provide a general template for quantifying many other eco‐geomorphic systems on the Earth's surface. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Forced vertical and horizontal movements of a rectangular rigid foundation on a transversely isotropic half‐space     

Morteza Eskandari‐Ghadi  Azizollah Ardeshir‐Behrestaghi  Ronald Y. S. Pak  Mostafa Karimi  Masoud Momeni‐Badeleh 《国际地质力学数值与分析法杂志》2013,37(14):2301-2320

An analytical investigation of a half‐space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape‐ and rigidity‐ induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point‐load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half‐space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two‐dimensional adaptive‐gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

古尔班通古特沙漠及周边区域冬季大气边界层高度对地表积雪的响应     

张梦肖  王豫  买买提艾力·买买提依明  刘永强  高佳程  肖婉秋  温聪  宋美琪  艾力亚尔·艾海提  王卫平  孟湘尧 《冰川冻土》2022,44(5):1558-1569

古尔班通古特沙漠是中国唯一冬季存在长期积雪的沙漠,在此特殊地理环境下,沙漠及周边区域冬季雪深和边界层高度的时空变化特征和相互关系尚未明确。本文利用1980—2019年SMMR（Scanning Multichannel Microwave Radiometer）、SSM/I（Special Sensor Microwave/Imager）、SSMI/S（Special Sensor Microwave Imager/Sounder）被动微波遥感雪深数据、古尔班通古特沙漠腹地雪深观测数据和ERA5再分析资料（the Fifth Generation ECMWF Reanalysis）边界层高度数据,分析了沙漠及周边区域冬季雪深和边界层高度的时空变化特征与相互关系。结果表明：古尔班通古特沙漠及周边区域冬季雪深年均值为8.45 cm,整体呈现东北部和南部积雪较深,其他区域积雪较浅并呈现出由沙漠中心区域向四周逐渐减少的特点,雪深在古尔班通古特沙漠及其东北、南边的邻近区域呈升高趋势,剩余地区呈下降趋势。古尔班通古特沙漠及周边区域冬季边界层高度年均值为105.54 m,呈现东南部和西北部高,中心沙漠区域、东北部、西南部较低的特点,边界层高度在沙漠及周边区域升高而其他区域降低。古尔班通古特沙漠的冬季雪深和大气边界层高度时空变化整体呈负相关,其中93.17%以上的沙漠区域呈负相关,平均相关系数为-0.32,最大相关系数绝对值为-0.58,空间相关系数为-0.42（P<0.05）。  相似文献   

基于最小作用原理的Richards方程变分解     

朱悦璐  陈磊 《岩土力学》2022,43(1):119-126

经典的Richards入渗控制方程属于偏微分方程,具有强烈的非线性,难以求得解析解。以入渗时间为最小作用量,基于Richards方程建立关于入渗路径的时间泛函,将考虑重力项的非饱和土垂直入渗问题转化为泛函极值问题,并构造等价的Euler-Lagrange方程进行求解。计算结果表明,扩散系数D（?）与概化湿润锋距离具有函数关系,当扩散系数D（?）形式已知时,可求得最优路径下湿润锋处含水率、较远处湿润锋最小含水率、土壤含水率最大熵分布3个问题,并基于最优路径检验了本研究条件下,Boltzmann变换和线性变换求解Richards方程的精度。求解过程未引进新变量化简Richards方程,不改变原方程结构,因此其解具有普遍性,可作为非饱和土力学计算的一个补充。  相似文献