非线性Lyapunov稳定性及Stern''''s Modons的稳定性判据

本文在构造正压大气运动的浅水波模式的Hamilton守恒量和积分不变的Casimir泛函的基础上,建立了一个积分不变的Lyapunov函数,通过使用变分法,找出了正压旋转流体运动的非线性Lyapunov稳定性判据,并进一步讨论了Stern's Modons的稳定性。     

Cross-equatorial structures of equatorially trapped nonlinear Rossby waves

Analysis of the Sea Surface Height (SSH) from satellite altimeters has shown that equatorially trapped Rossby waves exhibit asymmetric cross-equatorial structures; their northern extrema are much larger in magnitude than their southern counterparts. Such asymmetry is inconsistent with the classical theory for the first baroclinic, first meridional equatorially trapped Rossby mode, which predicts that SSH and zonal velocity are symmetric in latitude and the meridional velocity is latitudinally antisymmetric (Matsuno, 1966). Chelton et al. (2003) attributed the observed asymmetry to the mean-shear-induced modifications of first meridional mode Rossby waves. The present paper examines nonlinear rectification of cross-equatorial wave structures in the presence of different zonal mean currents. Nonlinear traveling Rossby waves embedded in shears are calculated numerically in a 1.5-layer model. Nonlinearity is shown to increase the cross-equatorial asymmetry substantially making the northern extrema even more pronounced. However, nonlinearity only slightly increases the magnitude of the westward phase speed.     

往复活塞式制冷压缩机性能系数的曲面回归方程

采用非线性二乘法对国产１２．５系列往复活塞式制冷压缩机的实测性能数据进行拟合，得出描述该系列制冷压缩机性能系数与运行工况之间相关关系的曲面回归方程，为制冷系统的数值计算、动态特性模拟和优化设计提供数学模型。     

Low correlation between redshift and intrinsic brightness for quasars and galaxies in a de sitter universe

Since the discovery of quasars, it has been recognized that these objects must have either an extraordinary intrinsic brightness or a nonlinear redshift. The most widely accepted current belief incorporates a linear (Hubble) redshift- distance relation and time evolution within a Big Bang model. We reconsider the possibility of a nonlinear (de Sitter) redshift-distance relation and find quasar intrinsic brightness to be not at all extraordinary. Given a de Sitter law, intrinsic brightness is found to be independent of redshift over five orders of magnitude.     

地形作用下有限振幅Rossby波的稳定性分析

本文用微分方程定性理论方法分析了地形对有限振幅Rossby波的稳定性影响。结果表明:地形北坡有利于波动出现不稳定,南坡使波动稳定;西坡使导式波动不稳定但使曳式波动稳定,东坡使导式波动稳定但使曳式波动不稳定。     

Stochastic analysis of spatial variability in unconfined groundwater flow

In this paper, spatial variability in steady one-dimensional unconfined groundwater flow in heterogeneous formations is investigated. An approach to deriving the variance of the hydraulic head is developed using the nonlinear filter theory. The nonlinear governing equation describing the one-dimensional unconfined groundwater flow is decomposed into three linear partial differential equations using the perturbation method. The linear and quadratic frequency response functions are obtained from the first- and second-order perturbation equations using the spectral method. Furthermore, under the assumption of the exponential covariance function of log hydraulic conductivity, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the linear system are derived. The results show that the variance derived herein is less than that of Gelhar (1977). The reason is that the log transmissivity is linearized in Gelhars work. In addition, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the quadratic system are derived as well. It is found that the correlation scale and the trend in mean of log hydraulic conductivity are important to the dimensionless variance ratio.     

Mapping nonlinear shallow-water tides: a look at the past and future

Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost’s complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions. While M can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems. In memory of Christian Le Provost     

Effect of perturbations on the non linear stability of triangular points in the restricted three-body problem with variable mass

The effect of small perturbations ε and ε ^′ in the Coriolis and the centrifugal forces, respectively on the nonlinear stability of the triangular points in the restricted three-body problem with variable mass has been studied. It is found that, in the nonlinear sense, the triangular points are stable for all mass ratios in the range of linear stability except for three mass ratios, which depend upon ε, ε ^′ and β, the constant due to the variation in mass governed by Jeans’ law.     

Linear and nonlinear vibration of non-uniform beams on two-parameter foundations using p-elements

A hierarchical finite element is presented for the geometrically nonlinear free and forced vibration of a non-uniform Timoshenko beam resting on a two-parameter foundation. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem. With the enriching degrees of freedom, the accuracy of the computed results and the computational efficiency are greatly improved. The arc-length iterative method is used to solve the nonlinear eigenvalue equation. The computed results of linear and nonlinear vibration analyses show that the convergence of the proposed element is very fast with respect to the number of Legendre orthogonal polynomials used. Since the elastic foundation and the axial load applied at both ends of the beam affect the ratios of linear frequencies associated with the internal resonance, they influence the nonlinear vibration characteristics of the beam. The axial tensile stress of the beam in nonlinear vibration is investigated in this paper, and attention should be paid to the geometrically nonlinear vibration resulting in considerably large axial tensile stress in the beam.     

Experimental investigation of the harmonic generation by waves over a submerged plate

Experiments in a wave flume have been performed to analyse the nonlinear interaction between regular gravity waves and a submerged horizontal plate used as breakwater. A new method, based on the Doppler shift generated by a moving probes, has been used to discriminate the incident fundamental mode and the reflected fundamental mode. The relationships of the reflection and transmission coefficients to the wave number at different submergence depth ratios are presented. The accurate discrimination, by this method, of the phase-locked and free modes allows the quantification of the higher harmonics generated by the breakwater and the analysis of the nonlinear interaction between the waves and the submerged plate. The transfer of energy from the fundamental mode to higher harmonics is very large in the cases of small submergence depth ratios. The vortices produced at the edges take part in the production of higher harmonics by interaction with the free surface but involve, at the same time, a dissipation process that increases the efficiency of the breakwater.