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1.
This paper presents a method to calculate finite-time Lyapunov exponents (FTLEs) for experimental time series using numerical simulation to approximate the local Jacobian of the system at each time step. This combined numerical–experimental approach to the calculation of FTLE is applicable to any physical system which can be numerically approximated. By way of example, the method is applied to the problem of vessel capsize. 相似文献
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E. Lohinger C. Froeschlé R. Dvorak 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):315-322
The Lyapunov characteristic numbers (LCNs) which are defined as the mean value of the distribution of the local variations of the tangent vectors to the flow (=ln
k
i
) (see Froeschlé, 1984) have been found to be sensitive indicators of stochasticity. So we computed the distribution of these local variations and determined the moments of higher order for the integrable and stochastic regions in a binary star system with =0.5. 相似文献
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地下水水位时间序列中的混沌特征 总被引:20,自引:0,他引:20
利用相空间重构技术、G -P算法以及Wolf提出的从单变量中提取Lyapunov指数的方法 ,分别计算了太原盆地 4组地下水水位时间序列的关联维数和Lyapunov指数。结果揭示在自然状态下 ,太原盆地某些孔隙潜水和孔隙承压水水位变化存在明显的混沌特征。这不仅为以后建立水位预测模型提供了理论依据 ,并且也为运用分形理论研究地质参数的时空变异性以及含水层结构的自相似性提供了进一步的支持。 相似文献
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In this paper, the four-dimensional variational data assimilation technique (4D-VAR) is presented as a tool to forecast floods. Our study is limited to purely hydrological flows and supposes that the weather, here a big rain, has been already forecasted by meteorological services. The technique consists in minimizing, in the sense of Lagrange, the cost function: a measure of the difference between calculated data and available observations, here the water level. This is done under constraints that are the equations of the physical model. In our case, we modified the shallow-water equations to include a simplified sediment transport model. The steepest descent algorithm is then used to find the minimum. This is made possible because we can compute analytically the gradient of the cost function by using the adjoint equations of the model. As an application of the 4D-VAR technique, the overflowing of the Chicoutimi River at the Chute-Garneau dam, during the 1996 flood, is investigated. It is found that the 4D-VAR method reduces the error in the water height forecast even when the erosion model is not activated. In terms of Lyapunov exponents, we estimate the predictability horizon of such an event to be about half-an-hour after a big rain. However, this limit of predictability can be increased by using more observations or by using a finer computational grid. 相似文献
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The role of sea surface temperature (SST) forcing in the development and predictability of tropical cyclone (TC) intensity is examined using a large set of idealized numerical experiments in the Weather Research and Forecasting (WRF) model. The results indicate that the onset time of rapid intensification of TC gradually decreases, and the peak intensity of TC gradually increases, with the increased magnitude of SST. The predictability limits of the maximum 10 m wind speed (MWS) and minimum sea level pressure (MSLP) are ~72 and ~84 hours, respectively. Comparisons of the analyses of variance for different simulation time confirm that the MWS and MSLP have strong signal-to-noise ratios (SNR) from 0-72 hours and a marked decrease beyond 72 hours. For the horizontal and vertical structures of wind speed, noticeable decreases in the magnitude of SNR can be seen as the simulation time increases, similar to that of the SLP or perturbation pressure. These results indicate that the SST as an external forcing signal plays an important role in TC intensity for up to 72 hours, and it is significantly weakened if the simulation time exceeds the predictability limits of TC intensity. 相似文献
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为了探究海表温度和海面高度之间的瞬时相关性,介绍了一种卫星测高数据的拉格朗日分析指数--有限尺度李雅普诺夫指数(Finite Size Lyapunov Exponent,FSLE),以黑潮延伸体区域的涡旋和南大西洋的亚南极锋为例,通过对观测、模式结果和融合产品结果的分析,探讨了该指数与海表温度梯度(Sea Surface Temperature Gradient,SSTG)之间的相关性。比较FSLE图像和SSTG图像发现,FSLE与SSTG均呈丝状结构,对海洋表层水体结构描述具有一致性,尤其在温度梯度大和地转流强的区域更为一致。二者的一致性要远好于其他常用方式,比如全流速、OW参数涡旋识别方法和Winding-Angle涡旋识别方法。不同区域FSLE与SSTG之间的相关性表现不同,黑潮延伸体区域相关系数存在显著的季节变化,而南大西洋亚南极锋区域季节内变化突出。 相似文献
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This paper addresses the problem of simultaneous depth tracking and attitude control of an underwater towed vehicle. The system proposed uses a two-stage towing arrangement that includes a long primary cable, a gravitic depressor, and a secondary cable. The towfish motion induced by wave driven disturbances in both the vertical and horizontal planes is described using an empirical model of the depressor motion and a spring-damper model of the secondary cable. A nonlinear, Lyapunov-based, adaptive output feedback control law is designed and shown to regulate pitch, yaw, and depth tracking errors to zero. The controller is designed to operate in the presence of plant parameter uncertainty. When subjected to bounded external disturbances, the tracking errors converge to a neighbourhood of the origin that can be made arbitrarily small. In the implementation proposed, a nonlinear observer is used to estimate the linear velocities used by the controller thus dispensing with the need for costly sensor suites. The results obtained with computer simulations show that the controlled system exhibits good performance about different operating conditions when subjected to sea-wave driven disturbances and in the presence of sensor noise. The system holds promise for application in oceanographic missions that require depth tracking or bottom-following combined with precise vehicle attitude control. 相似文献
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