On the growth of disturbances to forced and dissipated barotropic flows

Abstract

We consider the growth of disturbances to large-scale zonally-asymmetric steady states in a truncated spectral model for forced and dissipated barotropic flow. A variant of the energy method is developed to optimize the instantaneous disturbance energy growth rate. The method involves solving a matrix eigenvalue problem amenable to standard numerical techniques. Two applications are discussed. (1) The global stability of a family of steady states is assessed in terms of the Ekman damping coefficient r. It is shown that monotonic global stability (i.e., every disturbances energy monotonically decays to zero) prevails when r≥r_c . (2) Initially fastest-growing disturbances are constructed in the r<r_c regime. Particular attention is paid to a subregion of the r<r_c regime where initially-growing disturbances exist despite stability with respect to normal modes. Nonlinear time-dependent simulations are performed in order to appraise the time evolution of various disturbances.     

气温对太湖蓝藻复苏和休眠进程的影响

利用2005 2014年每日的卫星数据、气象站和浮标站观测资料研究复苏期和休眠期的平均气温、稳定通过界限温度初终日、周有效积温与太湖蓝藻休眠和复苏时间的关系,探讨气温是否是影响蓝藻休眠和复苏时间进程的关键因子.分析结果显示:太湖蓝藻复苏早晚与春季(3 5月)气温密切相关,春季气温越高,蓝藻复苏时间越早;太湖蓝藻休眠时间与秋、冬季(11次年1月)气温密切相关,秋、冬季气温越高,蓝藻休眠时间越晚.此外根据分析结果发现,太湖首次出现蓝藻水华的时间一般是气温稳定通过9℃初日之后的1个月左右,但上一周期的休眠与下一周期的复苏之间气温异常偏高会导致蓝藻水华首次出现时间早于稳定通过9℃初日;最后一次蓝藻水华出现时间与气温稳定通过4℃的终日相近;在复苏期,湖水中的叶绿素a浓度随周有效积温变化而变化,二者相关系数为0.9.     

Analysis of implicit HHT‐α integration algorithm for real‐time hybrid simulation

Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real‐time hybrid simulation. The implicit HHT α‐algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real‐time hybrid simulation. Consequently, the HHT α‐algorithm has been implemented for real‐time hybrid simulation using a fixed number of substep iterations. The resulting HHT α‐algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT α‐algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT α‐algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time‐step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT α‐algorithm with a fixed number of substep iterations. Both numerical and real‐time hybrid simulations are conducted to verify the modified algorithm. The experimental results demonstrate the effectiveness of the modified algorithm for real‐time testing. Copyright © 2011 John Wiley & Sons, Ltd.     

A model for grain-size sorting over tidal sand ridges

A model was developed and analyzed to quantify the effect of graded sediment on the formation of tidal sand ridges. Field data reveal coarse (fine) sediment at the crests (in the troughs), but often phase shifts between the mean grain-size distribution and the bottom topography occur. Following earlier work, this study is based on a linear stability analysis of a basic state with respect to small bottom perturbations. The basic state describes an alongshore tidal current on a coastal shelf. Sediment is transported as bed load and dynamic hiding effects are accounted for. A one-layer model for the bed evolution is used and two grain size classes (fine and coarse sand) are considered. Results indicate an increase in growth and migration rates of tidal sand ridges for a bimodal mixture, whilst the wavelength of the ridges remains unchanged. A symmetrical externally forced tidal current results in a grain-size distribution which is in phase with the ridges. Incorporation of an additional external M₄ tidal constituent or a steady current results in a phase shift between the grain-size distribution and ridge topography. These results show a general agreement with observations. The physical mechanism responsible for the observed grain-size distribution over the ridges is also discussed.Responsible Editor: Jens Kappenberg     

波动有限元方程显式逐步积分格式稳定性分析

对常用的波动有限元方程的两种显式格式的稳定性进行了分析,利用单元的最大频率乃是系统的特征频率的上界的概念结合模态分析方法,给出了便于实际应用的稳定性必要条件。同时,利用Von Neumann方法给出了这两种格式稳定性的充分条件,并通过算例对这两种稳定性条件进行验证。     

长白山天池火山西南麓水压致裂法地应力测量及其实测数据在断裂稳定性分析中的应用

长白山天池火山是一座新生代多成因复合火山, 其活动性一直受到地学界的高度重视.而地应力测量数据对于了解火山的活动情况等具有重要意义, 但目前长白山天池火山地区实测地应力资料较少.为了更准确地了解长白山天池火山地区现今地应力状态及断裂稳定性, 在长白山天池火山西南麓MJZ测点0~300 m孔深开展了水压致裂法地应力测量.利用此次实测地应力数据, 本文首先分析了该地区地壳浅表层应力状态, 结果表明: ①测区以水平构造应力为主导, 应力值与其他地区相比, 相对较低; ②S_H(最大水平主应力)、S_h(最小水平主应力)和S_v(垂向主应力)均随深度增加而基本呈线性增大趋势; 在60~180 m深度, 三者展现为逆断层应力状态, 即S_H＞S_h＞S_v; 在180~300 m, 则表现为S_H＞S_v＞S_h, 该应力关系有利于走滑断层活动; ③钻孔上部S_H方向为N38°E, 与东北地区构造应力场方向基本一致.钻孔下部由于受区内NW向断裂和其他因素影响, 存在与区域主应力方向有偏差的局部应力场.其次, 基于实测应力数据, 应用库仑摩擦滑动准则, 并取摩擦系数为0.6和1.0, 初步评价了区域断裂的稳定性.结果显示, 研究区现今应力状态尚未达到断裂失稳滑动水平, 推测测区断裂目前相对稳定.结合其较低的应力积累水平, 一定程度上反映出长白山天池火山区目前没有明显活动, 地壳总体是稳定的.本文的研究结果可为长白山天池火山的活动性、地震地质等研究提供地应力方面的基础数据, 同时也为测区地质环境安全评价提供参考依据.

     

黏性土坡地震失稳机制及其在黄土斜坡地震稳定性分析中的应用

基于地震作用下黏性土坡失稳滑动特点,以土体应力状态及其变化分析边坡失稳过程。通过分析地震作用下边坡不同部位土体应力状态和剪应力变化,结合实际地震边坡失稳破坏特征,提出黏性土坡地震三段式滑动失稳机制。在分析该滑动失稳机制与有限元强度折减法之间应力关联的基础上,将两者结合应用于实际黄土地震滑坡动力稳定性分析。依据此考虑得到的动力安全系数相比较其他方法,与极限平衡法得到的结果更为接近。     

Optimum design and application of non‐traditional tuned mass damper toward seismic response control with experimental test verification

A variant type of tuned mass damper (TMD) termed as ‘non‐traditional TMD (NTTMD)’ is recently proposed. Mainly focusing on the employment of TMD for seismic response control, especially for base‐isolated or high‐rise structures, this paper aims to derive design formulae of NTTMDs based on two methodologies with different targets. One is the fixed points theory with the performance index set as the maximum magnitude of the frequency response function of the relative displacement of the primary structure with respect to the ground acceleration, and the other is the stability maximization criterion (SMC) to make the free vibration of the primary structure decay in the minimum duration. Such optimally designed NTTMDs are compared with traditional TMDs by conducting both numerical simulations and experiments. The optimum‐designed NTTMDs are demonstrated to be more effective than the optimum‐designed traditional TMDs, with smaller stroke length required. In particular, the effectiveness of the TMDs combined with a base‐isolated structure is investigated by small‐scale model experimental tests subjected to a time scaled long period impulsive excitation, and it is demonstrated that the SMC‐based NTTMD can suppress structural free vibration responses in the minimum duration and requires much smaller accommodation space. Additionally, a small‐scale shaking table experiment on a high‐rise bending model attached with a SMC‐based NTTMD is conducted. This study indicates that NTTMD has a high potential to apply to seismic response control or retrofit of structures such as base‐isolated or central column‐integrated high‐rise structures even if only a limited space is available for accommodating TMDs. Copyright © 2015 John Wiley & Sons, Ltd.     

A parameterization of the wavelength of tidal dunes

The idealized model of Besio et al. (On the formation of sand waves and sand banks. Journal of Fluid Mechanics 2006; 557: 1–17) is used to predict the wavelength of tidal dunes (sand waves) generated by tidal currents in estuaries and shallow seas. The predictions are then analysed and a formula is proposed to estimate the wavelength of tidal dunes as a function of the parameters of the problem. The wavelength of the dunes is found to increase when the water depth is increased and/or the strength of the tidal current is decreased. On the other hand, the size of the bottom material (if medium sand is considered) and the tidal ellipticity are found to have a relatively small influence on the length of the bottom forms. The formula proposed provides results which are consistent with field observations of different authors. Copyright © 2011 John Wiley & Sons, Ltd.