Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary *** I:Theory and Integral Formulae

作     者：Qin XU 高守亭 曹洁 

作者机构：NOAA/National Severe Storms Laboratory Norman Oklahoma USA Cooperative Institute for Mesoscale Meteorological Studies University of Oklahoma USA Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 （Received 15 October 2010 revised 9 March 2011） 

出 版 物：《Advances in Atmospheric Sciences》 (大气科学进展（英文版）)

年 卷 期：2011年第28卷第6期

页      面：1433-1444页

核心收录：

学科分类：07[理学] 08[工学] 0824[工学-船舶与海洋工程] 0701[理学-数学] 082401[工学-船舶与海洋结构物设计制造] 070101[理学-基础数学] 

基　　金：supported by the Office of Naval Research (Grant No. N000141010778) to the University of Oklahoma the National Natural Sciences Foundation of China (Grant Nos. 40930950,41075043,and 4092116037) to the Institute of Atmospheric Physics provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement (No. NA17RJ1227),U.S. Department of Commerce 

主　　题：integral formulae streamfunction velocity potential domain of arbitrary shape 

摘      要：The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic *** integral formulas and their variants are used to formulate solutions for the coupled *** the absence of data holes,the total solution is the sum of two integral *** is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components（velocity potential and streamfunction） can be constructed by applying Green＇s function for Poisson equation in unbounded domain to the divergence and vorticity inside the *** other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the *** setting either the velocity potential（or streamfunction） component to zero,the other component of the externally induced solution can be expressed by the imaginary（or real） part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced *** streamfunction（or velocity potential） for the externally induced solution can also be expressed by the boundary integral of a double-layer（or singlelayer） density *** the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.