Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which t...Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.展开更多
Based on the internal temperature variation of a dam lagging behind the ambient temperature variation,the ambient temperature of continuous variation is disctetized,and the functional expression of the thermal displac...Based on the internal temperature variation of a dam lagging behind the ambient temperature variation,the ambient temperature of continuous variation is disctetized,and the functional expression of the thermal displacement component of the dam caused by single instantaneous temperature variation is obtained.Considering the temporal and spatial distribution law of the ambient temperature and its relation with air and water temperature,the function is expanded into a Taylor series.As a result,the improved thermal displacement component expression for a dam monitoring model is obtained.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002098 and 11332007)
文摘Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51079046,50909041,51139001)the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cyclein River Basin (Grant No. IWHR-SKL-201108)+4 种基金the Special Fund of State Key Laboratory of China (Grant Nos. 2009586012,2009586912,201058-5212)the Fundamental Research Funds for the Central Universities(Grant Nos. 2009B08514,2010B20414,2010B01414,2010B14114)Jiangsu Province "333 High-Level Personnel Training Project" (Grant No.2017-B08037)Graduate Innovation Program of Universities in Jiangsu Province (Grant No. CX09B_163Z)the Science Foundation for the Excellent Youth Scholars of Ministry of Education of China (Grant No.20070294023)
文摘Based on the internal temperature variation of a dam lagging behind the ambient temperature variation,the ambient temperature of continuous variation is disctetized,and the functional expression of the thermal displacement component of the dam caused by single instantaneous temperature variation is obtained.Considering the temporal and spatial distribution law of the ambient temperature and its relation with air and water temperature,the function is expanded into a Taylor series.As a result,the improved thermal displacement component expression for a dam monitoring model is obtained.
