平面边界前Stokes流动基本的奇异性

Stokes Flow Due to Fundamental Singularities Before a Plane Boundary

Department of Mathematics, Shahjalal University of Science and Technology, Sylhet Bangladesh;

摘要: 利用双调和函数A和调和函数B，给出了三维Stokes流动速度场和压力场的描述．由此建立了计算区域边界为固定无滑移平面边界Stokes流动基本奇异性的一般定理．刚性平面前轴对称Stokes流动的Collins定理成为本文定理的特例．给出的几个例证说明了方法的有效性．
- Stokes流动 /
- Stokeslet /
- 傅里叶变换 /
- 调和函数 /
- 双调和函数
Abstract: A representation for the velocity and pressure fields in three dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B.This representation was used to establish a general theorem for the calculation of Stokes flow due to fundamental singularities in a region bounded by a stationary no-slip plane boundary.Collins's theorem for axisymmetric Stokes flow before a rigid plane follows as a special case of the the orem.A few illustrative examples are given to show its usefulness.
- Stokes flow /
- Stokeslet /
- Fouries transform /
- harmonic function /
- biharmonic function

[1]	Chwang A T,Wu T Y.Hydromechanics of low-Reynolds numer flow,Part 2:Singularity method for Stokes flows[J].J Fluid Mech,1975,67:787—815. doi: 10.1017/S0022112075000614
[2]	Collins W D.A note on Stokes's stream function for the slow steady motion of viscous fluid before plane and spherical boundaries[J].Mathematika,1954,1:125—130. doi: 10.1112/S0025579300000607
[3]	Collins W D.Note on a sphere theorem for the axisymmetric Stokes flow of a viscous fluid[J].Mathematika,1958,5:118—121. doi: 10.1112/S0025579300001431
[4]	Blake J R.A note on the image system for a Stokeslet in a no-slip boundary[J].Proc Camb Phil Soc,1971,70:303—310. doi: 10.1017/S0305004100049902
[5]	Blake J R,Chwang A T.Fundamental singularities of viscous flow,Part 1:The image systems in the vicinity of a stationary no-slip boundary[J].J Eng Math,1974,8:23—29. doi: 10.1007/BF02353701
[6]	Palaniappan D,Nigam S D,Amaranath T,et al.Lamb's solution of Stokes's equations:A sphere theorem[J].Q JL Mech Appl Math,1992,45(1):47—56. doi: 10.1093/qjmam/45.1.47
[7]	Chowdhury G A H,Sen S K.Stokes flow before a plane boundary[J].Indian J Pure Appl Math(to be published)
[8]	Happel J,Brenner H.Low Reynolds Number Hydrodynamics[M].4th print.Dordrecht:Martinus Nijhoff Publishers,1986.