Quadratic correction to the linear wave spectrum of two-dimensional random waves

ImooUcrIONAtfrequendesseveraltirathatofthespeCtralpcak,thewaveelevationhigherordercomPonentS'contributionstothewavespatrumaremoresignificantthanthosefromthelinearcomPonentS.Tick(l959)firstproposedandevaluatedtheserendxidespodrumofunidindionalrandomwaves.TheexpnaionderivedbyDingPingxingetal.(l994)forthesecondxirderspeCtmmisanimProvernentofTick's.TickandDingPingxingetal.didnotaanuntforthirdxirderperturbations,althoughthethirdxirdersolutionefhaonthequadraticspeCtrumisofthesameorderofmagnit…     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

The role of moisture fluctuations in unsaturated transport

Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with a finite correlation scale of log-hydraulic conductivity is analyzed. The effects of spatial variability of the moisture distribution parameter on the asymptotic spreading behavior of a unsaturated solute plume are assessed. This is accomplished by comparing two asymptotic macrodispersivities and two variance of solute concentration, obtained for a constant moisture content and spatially varied moisture, respectively.     

主动变刚度结构的动力卸载效应

本文讨论了主动变刚度结构体系AVS(Active Variable Stiffness)的动力卸载效应。结构体系中的AVS控制器关闭或开启瞬时，结构系统刚度分布发生突变，通常也伴随着对系统的能量输入或输出，使得该瞬时结构体系相应受到—加速度增量作用，此增量的方向与结构加速度方向相反，能有效地抑制结构体系的刚度不变层向刚度突变层的动力卸载。此外，文中分析了AVS控制器闭合或开启引起的结构体系相对于原结构的第i阶自振频率摄动，进而讨论了AVS控制器的开关控制律和结构的自振频率摄动及动力卸载效应的相互关系。理论分析和计算结果表明：在合理的结构变形位置闭合或开启AVS控制器，动力卸载效应对结构体系的不利作用及结构体系的频率特性相对于原结构改变很小。     

Spacecraft potential control aboard Equator-S as a test for Cluster-II

The payload of Equator-S was complemented by the potential control device (PCD) to stabilise the electric potential of the spacecraft with respect to the ambient plasma. Low potentials are essential for accurate measurements of the thermal plasma. The design of PCD is inherited from instruments for Geotail and Cluster and utilises liquid metal ion sources generating a beam of indium ions at several keV. The set-up of the instrument and its interaction with the plasma instruments on board is presented. When the instrument was switched on during commissioning, unexpectedly high ignition and operating voltages of some ion emitters were observed. An extensive investigation was initiated and the results, which lead to an improved design for Cluster-II, are summarised. The cause of the abnormal behaviour could be linked to surface contamination of some emitters, which will be monitored and cured by on-board procedures in future. The mission operations on Equator-S were not at all affected, because of the high redundancy built into the instrument so that a sufficient number of perfectly operating emitters were available and were turned on routinely throughout the mission. Observations of the effect of spacecraft potential control on the plasma remained limited to just one event on January 8, 1998, which is analysed in detail. It is concluded that the ion beam lead to the predicted improvement of the particle measurements even outside the low density regions of the magnetosphere where the effect of spacecraft potential control would have been much more pronounced, and that the similar instruments for the four Cluster-II spacecraft to be launched in 2000 will be very important to ensure accurate plasma data from this mission.     

Linearized amplitude variation with offset and azimuth and anisotropic poroelasticity

The normal-to-shear weakness ratio is commonly used as a fracture fluid indicator, but it depends not only on the fluid types but also on the fracture intensity and internal architecture. Amplitude variation with offset and azimuth is commonly used to perform the fluid identification and fracture characterization in fractured porous rocks. We demonstrate a direct inversion approach to utilize the observable azimuthal data to estimate the decoupled fluid (fluid/porosity term) and fracture (normal and shear weaknesses) parameters instead of the calculation of normal-to-shear weakness ratio to help reduce the uncertainties in fracture characterization and fluid identification of a gas-saturated porous medium permeated by a single set of parallel vertical fractures. Based on the anisotropic poroelasticity and perturbation theory, we first derive a linearized amplitude versus offset and azimuth approximation using the scattering function to decouple the fluid indicator and fracture parameters. Incorporating Bayes formula and convolution theory, we propose a feasible direct inversion approach in a Bayesian framework to obtain the direct estimations of model parameters, in which Cauchy and Gaussian distribution are used for the a priori information of model parameters and the likelihood function, respectively. We finally use the non-linear iteratively reweighted least squares to solve the maximum a posteriori solutions of model parameters. The synthetic examples containing a moderate noise demonstrate the feasibility of the proposed approach, and the real data illustrates the stabilities of estimated fluid indicator and dry fracture parameters in gas-saturated fractured porous rocks.     

Upstream perturbation and floodplain formation effects on chute-cutoff-dominated meandering river pattern and dynamics

A sustained dynamic inflow perturbation and bar–floodplain conversion are considered crucial to dynamic meandering. Past experiments, one-dimensional modelling and linear theory have demonstrated that the initiation and persistence of dynamic meandering require a periodic transverse motion of the inflow. However, it remains unknown whether the period of the inflow perturbation affects self-formed meander dynamics. Here, we numerically study the effect of the inflow perturbation period on the development and meander dynamics of a chute-cutoff-dominated river, which requires two-dimensional modelling with vegetation forming floodplain on bars. We extended the morphodynamic model Nays2D with growth and mortality rules of vegetation to allow for meandering. We tested the effect of a transversely migrating inflow boundary by varying the perturbation period between runs over an order of magnitude around typical modelled meander periods. Following the cutoff cascade after initial meander formation from a straight channel, all runs with sufficient vegetation show series of growing meanders terminated by chute cutoffs. This generates an intricate channel belt topography with point bar complexes truncated by chutes, oxbow lakes, and scroll-bar-related vegetation age patterns. The sinuosity, braiding index and meander period, which emerge from the inherent biomorphological feedback loops, are unrelated to the inflow perturbation period, although the spin-up to dynamic equilibrium takes a longer time and distance for weak and absent inflow perturbations. This explains why, in previous experimental studies, dynamic meandering was only accomplished with a sustained upstream perturbation in flumes that were short relative to the meander wavelength. Our modelling of self-formed meander patterns is evidence that scroll-bar-dominated and chute-cutoff-dominated meanders develop from downstream convecting instabilities. This insight extends to many more fluvial, estuarine and coastal systems in morphological models and experiments, which require sustained dynamic perturbations to form complex patterns and develop natural dynamics. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.     

Elliptic-type motion in Fock's gravitational field

The elliptic-type motion in the gravitational field found by Fock as exact solution of Einstein's vacuum equations in the case of spherical symmetry (Solution called here Fock's gravitational field) is studied by means of a classic method based on the perturbation theory. Regarding the deviations of the orbit from a Kepleian orbit as perturbations, the first and second order variations of the Keplerian orbital elements over one nodal period as well as those of the nodal period itself are determined.