Broken ergodicity,magnetic helicity,and the MHD dynamo

We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory.     

磁场散度为零的变分重构法在日冕太阳风数值模拟中的应用

本文利用保持平均磁场散度为零的限制条件,设计出了满足全局散度为零的变分重构方法（Globally solenoidality-preserving variational reconstruction approach,VR-GSP）,并将其应用于日冕太阳风磁流体力学（Magnetohydrodynamics,MHD）数值模拟中的磁场重构.为评估该方法的有效性,我们模拟了2234卡林顿周（Carrington rotation,CR）的日冕结构.在模拟中,我们将VR-GSP方法与Feng等（2019）中的基于最小二乘法的全局磁场散度为零的重构方法（Globally solenoidality-preserving least-squares method,LSQ-GSP）作了比较.比较结果显示,基于VR-GSP方法的MHD模拟同样再现了Solar Dynamics Observatory（SDO）卫星、Solar and Heliospheric Observatory（SOHO）飞船以及Wind卫星观测到的包括冕流以及高低速流等大尺度日冕结构,而且相比于LSQ-GSP,基于VR-GSP的MHD模拟的计算效率更高,从而也说明其更有助于在有限体积框架下设计出满足磁场散度为零的高效和紧致的数值方法,并应用于研究复杂强磁场环境下的磁流体力学问题.

     

A high order WENO finite difference scheme for incompressible fluids and magnetohydrodynamics

We present a high order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of incompressible fluid dynamics and magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme that has been successfully applied to compressible fluids, with or without magnetic fields. A fractional time-step method is used to enforce the incompressibility condition. Two basic elements of the WENO scheme, upwinding and wave decomposition, are shown to be important in solving the incompressible systems. Numerical results demonstrate that the scheme performs well for one-dimensional Riemann problems, a two-dimensional double-shear flow problem, and the two-dimensional Orszag–Tang MHD vortex system. They establish that the WENO code is numerical stable even when there are no explicit dissipation terms. It can handle discontinuous data and attain converged results with a high order of accuracy.     

A cross entropy method for flood frequency analysis

The cross-entropy method with fractile constraints has been developed to estimate a random variable when the data are a set of independent observations of the variable. The method can claim several advantages over existing methods. It uses a reference distribution like the prior distribution in Bayesian analysis and likewise generates a posterior distribution.The method is of interest, in particular, because it satisfies two fundamental requirements for selfconsistency in the analysis of a probabilistic system based on data: a principle of invariance and a principle of data monotonicity.The method is applied to flood analysis. Robustness of the minimum cross-entropy method is compared with other methods: the methods of moments and the maximum likehood.     

A cost-benefit analysis for the implementation of riparian buffer strips in the Shihmen reservoir watershed

The Shihmen reservoir is an important water source for about 3.4 million people in northern Taiwan. To protect reservoir water quality,it is necessary to conserve and manage the associated watersheds. Riparian buffer strips can trap pollutants emitted near a watershed.The location and design of a buffer strip can influence its pollutant-trapping efficiency.Any commitment of land for use as a riparian buffer strip must consider the project’s economic effectiveness.The present research is a cost-benefit analysis of various possible land developments in the Shihmen reservoir watershed.This study has applied a regression equation to evaluate pollutant-trapping efficiency levels of riparian buffer strips of various widths.Planned buffer strips have been evaluated in terms of net economic effectiveness and benefit-cost ratio.Results indicate that the optimal buffer strip width is 30 m for the Shihmen reservoir watershed.     

一种考虑截面翘曲的剪力墙宏模型

提出了一种六自由度刚杆—弹簧单元，可以像有限元法那样根据精度和计算量的要求，以适当密度在水平和垂直方向拼装成剪力墙的宏模型。这一宏模型不仅可以反映中和轴的移动，而且不再受现有宏模型中平面假定的限制，可以反映初始平截面的剪切翘曲。这对于分析剪跨比较小的剪力墙是有一定必要性的。该模型竖向弹簧布置在Gauss积分点处，从而有效提高了计算精度和效率。利用该模型计算了五个剪力墙的弹塑性“推覆”过程，取得了与实验较为一致的结果。对一些有关宏模型中本构关系选取及变形假定的问题进行了讨论。     

Sensitivity equations for hyperbolic conservation law-based flow models

The present paper focuses on the governing equations for the sensitivity of the variables to the parameters in flow models that can be described by one-dimensional scalar, hyperbolic conservation laws. The sensitivity is shown to obey a hyperbolic, scalar conservation law. The sensitivity is a conserved scalar except in the case of discontinuous flow solutions, where an extra, point source term must be added to the equations in order to enforce conservation. The propagation speed of the sensitivity waves being identical to that of the conserved variable in the original conservation law, the system of conservation laws formed by the original hyperbolic equation and the equation satisfied by the sensitivity is linearly degenerate. A consequence on the solution of the Riemann problem is that rarefaction waves for the variable of the original equation result in vacuum regions for the sensitivity. The numerical solution of the hyperbolic conservation law for the sensitivity by finite volume methods requires the implementation of a specific shock detection procedure. A set of necessary conditions is defined for the discretisation of the source term in the sensitivity equation. An application to the one-dimensional kinematic wave equation shows that the proposed numerical technique allows analytical solutions to be reproduced correctly. The computational examples show that first-order numerical schemes do not yield satisfactory numerical solutions in the neighbourhood of moving shocks and that higher-order schemes, such as the MUSCL scheme, should be used for sharp transients.     

Determining the amplitude and timing of streamflow discontinuities: A cross wavelet analysis approach

Records of natural processes, such as gradual streamflow fluctuations, are commonly interrupted by long or short disruptions from natural non‐linear responses to gradual changes, such as from river‐ice break‐ups, freezing as a result of annual solar cycles, or human causes, such as flow blocking by dams and other means, instrument calibrations and failure. The resulting abrupt or gradual shifts and missing data are considered to be discontinuities with respect to the normal signal. They differ from random noise as they do not follow any fixed distribution over time and, hence, cannot be eliminated by filtering. The multi‐scale resolution features of continuous wavelet analysis and cross wavelet analysis were used in this study to determine the amplitude and timing of such streamflow discontinuities for specific wavebands. The cross wavelet based method was able to detect the strength and timing of abrupt shifts to new streamflow levels, gaps in data records longer than the waveband of interest and a sinusoidal discontinuity curve following an underlying modeled annual signal at ±0.5 year uncertainty. Parameter testing of the time‐frequency resolution demonstrated that high temporal resolution using narrow analysis windows is favorable to high‐frequency resolution for detection of waveband‐related discontinuities. Discontinuity analysis on observed daily streamflow records from Canadian rivers showed the following: (i) that there is at least one discontinuity/year related to the annual spring flood in each record studied, and (ii) neighboring streamflows have similar discontinuity patterns. In addition, the discontinuity density of the Canadian streamflows studied in this paper exhibit 11‐year cycles that are inversely correlated with the solar intensity cycle. This suggests that more streamflow discontinuities, such as through fast freezing, snowmelt, or ice break‐up, may occur during years with slightly lowered solar insolation. Copyright © 2013 John Wiley & Sons, Ltd.     

A compound method for random noise attenuation

Random noise attenuation, preserving the events and weak features by improving signal‐to‐noise ratio and resolution of seismic data are the most important issues in geophysics. To achieve this objective, we proposed a novel seismic random noise attenuation method by building a compound algorithm. The proposed method combines sparsity prior regularization based on shearlet transform and anisotropic variational regularization. The anisotropic variational regularization which is based on the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation attenuates noises while preserving the events of seismic data and it effectively avoids the fine‐scale artefacts due to shearlets from the restored seismic data. The proposed method is formulated as a convex optimization problem and the split Bregman iteration is applied to solve the optimization problem. To verify the effectiveness of the proposed method, we test it on several synthetic seismic datasets and real datasets. Compared with three methods (the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation, shearlets and shearlet‐based weighted anisotropic total variation), the numerical experiments indicate that the proposed method attenuates random noises while alleviating artefact and preserving events and features of seismic data. The obtained result also confirms that the proposed method improves the signal‐to‐noise ratio.     

A local model for analysis of pump and treat systems with vertical barrier walls

We present a mathematical model of local, steady groundwater flow near a vertical barrier wall. Flow features represented in the model include an impermeable arc-shaped barrier wall and multiple wells; distant boundary conditions are not included explicitly, but their effects on the local flow field are modelled by specifying a uniform flow at infinity and a constant areal recharge within a local domain. We develop an explicit closed-form solution to the boundary-value problem using the analytic element method. The solution is an extension of a harmonic solution presented by Anderson and Mesa [Anderson EI, Mesa E. The effects of vertical barrier walls on the hydraulic control of contaminated groundwater. Adv Water Resourc 2006;29(1):89–98] which does not include the effects of recharge. We demonstrate that the general solution with recharge consists of the harmonic solution superposed on a special case of the harmonic solution along with two elementary one-dimensional flow solutions. The results are used to investigate the effects of areal recharge on the capture zone envelopes of the pumping wells and on the reduction in discharge that can be achieved by including a barrier wall in a pump and treat design. We find that the benefits of including an open barrier wall in a design, measured as a reduction in the pumping rate required to contain a plume, increase for higher recharge rates. Dimensionless plots of capture zone envelopes are presented for a practical well and barrier wall configuration.     

A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical and geophysical MHD

We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transport” method, with additional continuity requirement on the magnetic field representation. The second ingredient in the MUSCL scheme is the predictor step that ensures second order accuracy both in space and time. We explore specific constraints that the mathematical properties of the induction equations place on this predictor step, showing that three possible variants can be considered. We show that the most aggressive formulations reach the same level of accuracy than the other ones, at a lower computational cost. More interestingly, these schemes are compatible with the Adaptive Mesh Refinement (AMR) framework. It has been implemented in the AMR code RAMSES. It offers a novel and efficient implementation of a second order scheme for the induction equation. The scheme is then adaptated to solve for the full MHD equations using the same methodology. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax–Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to the ABC dynamo problem and to the collapse of a magnetized cloud core.     

一种基于多项式外推的局部透射边界位移解(外行波为平面波情形)

基于外行波局部法向透射概念，从多项式外推的角度，结合一维和广义二维几何解释，推导建立了外行波为平面波时，人工边界节点位移解的计算公式。对该位移解的精度进行了时域分析，论证了该位移解收敛于数值精确解的必要条件和线性外推位移解的精度与数值精确解匹配的充要条件。在此基础上提出了一次“精确”透射的概念和相应的数学方法，实现了该位移解逼近于数值精确解的优化计算。     

一种基于多项式外推的局部透射边界位移解(外行波为非平面波情形)

一般情况下,通过人工边界向外透射的波动常为非平面波。对于近场非平面波在人工边界上的透射问题,不能采用简单的平面波透射方法。本文针对近场非平面波在人工边界上的透射特点,分析了非平面波沿人工边界法向视波速的变化规律及其近场失稳机制,推导了适合近场非平面波的、人工边界点位移解的不等步距线性外推公式。     

A climatic dataset of ocean vertical turbulent mixing coefficient based on real energy sources

Using data on wind stress, significant height of combined wind waves and swell, potential temperature, salinity and seawater velocity, as well as objectively-analyzed in situ temperature and salinity, we established a global ocean dataset of calculated wind- and tide-induced vertical turbulent mixing coefficients. We then examined energy conservation of ocean vertical mixing from the point of view of ocean wind energy inputs, gravitational potential energy change due to mixing (with and without artificially limiting themixing coefficient), and K-theory vertical turbulent parameterization schemes regardless of energy inputs. Our research showed that calculating the mixing coefficient with average data and artificial limiting the mixing coefficient can cause a remarkable lack of energy conservation, with energy losses of up to 90% and changes in the energy oscillation period. The data also show that wind can introduce a huge amount of energy into the upper layers of the Southern Ocean, and that tidesdo so in regions around underwater mountains. We argue that it is necessary to take wind and tidal energy inputs into account forlong-term ocean climate numerical simulations. We believe that using this ocean vertical turbulent mixing coefficient climatic dataset is a fast and efficient method to maintain the ocean energy balance in ocean modeling research.     

A variational method for correcting non-systematic errors in numerical weather prediction

A variational method based on previous numerical forecasts is developed to estimate and correct non-systematic component of numerical weather forecast error. In the method, it is assumed that the error is linearly dependent on some combination of the forecast fields, and three types of forecast combination are applied to identifying the forecasting error: 1) the forecasts at the ending time, 2) the combination of initial fields and the forecasts at the ending time, and 3) the combination of the forecasts at...     

局部指数标架小波束在复杂介质方向照明分析中的应用

提出了用局部指数标架小波束进行角度域分解的方法,解决了局部余弦基和局部正弦基缺乏单一方向性的问题.局部指数标架由局部余弦基和局部正弦基线性组合而成,是冗余度为2的紧标架.利用局部余弦变换和局部正弦变换的快速算法,能使基于局部指数标架进行方向照明分析的计算效率较常用的局部倾斜叠加和Gabor-Daubechies标架等方法具有更为明显的优势.通过计算二维SEG/EAGE模型和SIGSBEE模型的方向照明图以及采集系统倾角响应图证实了本文方法的有效性.该方法的高效性使其在三维模型的方向照明分析和大规模的工业应用中具有广阔前景.     

A combined local damage index for seismic assessment of existing RC structures

A new local damage index for existing RC structures is introduced, wherein deterioration caused by all deformation mechanisms (flexure, shear, anchorage slip) is treated separately for each mechanism. Moreover, the additive character of damage arising from the three response mechanisms, and the increase in degradation rate caused by their interaction, are fully taken into consideration. The proposed local damage index is then applied, in conjunction with a finite element model developed previously by the authors, to assess seismic damage response of several RC column and frame test specimens with substandard detailing. It is concluded that in all cases and independently from the prevailing mode of failure, the new local damage index describes well the damage pattern of the analysed specimens. Copyright © 2012 John Wiley & Sons, Ltd.     

重磁异常解释的归一化局部波数法

局部波数法是进行重磁数据解释的常用方法之一.本文提出归一化局部波数法,该方法在不需要任何关于地质体信息的前提下能有效地完成异常的反演工作,且给出了不同归一化方式的应用效果.理论模型试验表明归一化局部波数法能准确地完成异常的反演,且通过对比发现其他归一化方式（中值、几何平均和调和平均）的计算结果相对算术平均归一化结果具有更高的分辨率.将该方法应用于实测磁异常的解释,获得了未知地质体的空间位置.     

Simplified procedure for the estimation of local inelastic deformation demands for seismic performance assessment of buildings

The implementation of performance‐based design and assessment procedures in seismic codes leads to the need for an accurate estimation of local component demands. According to Part 3 of Eurocode 8 safety checks should be always conducted in terms of plastic rotations, even when linear elastic methods of analysis are used. This paper demonstrates that linear analysis fails to predict inelastic deformation demands at the member level. Therefore, a simplified procedure that allows for the estimation of beam inelastic deformation demands using linear elastic methods of analysis in a simple and conservative way is presented herein. A number of moment‐resisting steel frames designed according to different criteria and exhibiting different column‐to‐beam strength ratios were analysed and used for the derivation of the proposed procedure. A comparative study between alternative methods of quantifying inelastic deformation demands using linear analysis is also carried out. The results obtained allow concluding about the efficiency and conservativeness of the proposed procedure which makes it attractive to be employed in engineering practice. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal design of tuned mass dampers for a multi‐storey cross laminated timber building against seismic loads

In this paper, the effectiveness of different design solutions for tuned mass dampers (TMD) applied to high‐rise cross‐laminated (X‐Lam) timber buildings as a means to reduce the seismic accelerations was investigated. A seven‐storey full‐scale structure previously tested on shaking table was used as a reference. The optimal design parameters of the TMDs, i.e. damping and frequency ratios, were determined by using a genetic algorithm on a simplified model of the reference structure, composed by seven masses each representing one storey. The optimal solutions for the TMDs were then applied to a detailed finite element model of the seven‐storey building, where the timber panels were modelled with shell elements and the steel connectors with linear spring. By comparing the numerical results of the building with and without multiple TMDs, the improvement in seismic response was assessed. Dynamic time‐history analyses were carried out for a set of seven natural records, selected in accordance with Eurocode 8, on the simplified model, and for Kobe earthquake ground motion on the detailed model. Results in terms of acceleration reduction for different TMD configurations show that the behaviour of the seven‐storey timber building can be significantly improved, especially at the upper storeys. Copyright © 2016 John Wiley & Sons, Ltd.