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Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows

Science China(Physics,Mechanics & Astronomy) 2005年第2期48卷 228-236页

作者： LUO Jisheng, WANG Xinjun & ZHOU Heng Department of Mechanics, Tianjin University Liu-Hui Center of Mathematics, Nankai and Tianjin University, Tianjin 300071, China Department of Mechanics Tianjin University Tianjin China Liu-Hui Center of Mathematics Nankai and Tianjin University Tianjin China

Laminar-turbulent transition is an old yet unsolved problem. Notwithstanding the great effort made, there is an important question that seems not to have been addressed yet, that is, what is the inherent mechanism of breakdown that eventually leads to transition? The conventional idea is that the transition starts from the amplification of disturbances, and when the disturbances become larger, higher harmonics will be generated due to nonlinear effect, making the flow more and more complicated, and finally turbulent. Though the scenario seems clear, yet there is a missing link, that is, what happens in the breakdown process. Here we show by analyzing the results from direct numerical simulations that the change of stability characteristics of the mean flow profile plays a key role in the breakdown process.

关键词： laminar-turbulent transition, breakdown, plane channel flow.

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ON THE breakdownS OF THE GALERKIN AND LEAST-SQUARES METHODS

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2002年第2期11卷 137-148页

作者： Zhong Baojiang(钟宝江) College of Science Nanjing University of Aero. & Astro. Nanjing 210016 PRC

The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.

关键词： large linear systems, iterative methods, Krylov subspace methods, Galerkin method, least-squares method, FOM , GMRES , breakdown, stagnation, restarting, preconditioners.

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Observations on the leader-return stroke of cloud-to-ground lightning with the broadband interferometer

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Science China Earth Sciences 2002年第3期45卷 259-269页

作者：董万胜刘欣生张义军张广庶 Cold and Arid Regions Environmental & Engineering Research Institute Chinese Academy of Sciences Lanzhou 730000 China School of Electrical Engineering Wuhan University Wuhan 430072 China

Radio frequency observations of cloud-to-ground lightning (CG) were made in 1999 in Guangdong Province with the broadband lightning interferometer. In this paper, radiation source locations and electric field waveforms are analyzed for different types of breakdown events, including the preliminary breakdown of in-cloud activities, the stepped leaders of initial strokes to ground and activities during and following return strokes. It is shown that the structure and development of lightning discharges and associated breakdown processes can be reconstructed by using this new type of lightning radiation source location system. The detectable radiation of lightning was primarily produced by the negative breakdown process. The channel was concentrated with few branches during the preliminary breakdown stage of CG lightning flashes. The radiation sources appeared generally at the tip of the channel. During the late period of the stepped leader, the radiation sources were dispersed with branches extended away from the main channel. The radiation sources were in a certain length segment of the channel and the altitude of the segment descended along with the propagation of the leader to the ground. During the preliminary breakdown and the stepped leader of initial strokes to the ground, a sequence of fast negative streamers were observed to start continually from or farther away the lightning-initiated region and propagate along the developed leader channel, which may supply negative charge that assisted the leader's development. The progression speed of fast negative streamers was about ten times faster than the average speed of lightning channel.

关键词： broadband interferometer, cloud-to-ground lightning, preliminary breakdown, stepped leader.

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