二层流体中沿任意路径运动的奇点解析解*
Analytical Solutions of Singularities Moving with an Arbitrary Path when Two Fluids Are Present
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摘要: 本文求解了二层流体存在时在上层或下层流体中沿任意路径运动的奇点的速度势.流体的深度为有限或者无限.计入上层流体的影响后,流体交界面不再是等压力面或零压力面.文中给出了这种情况下的一系列奇点基本解的解析表达式.Abstract: The derivations are carried out for the velocity potentials of singularities moving with an arbitrary path either in the upper fluid or in the lower fluid with or without a horizontal bottom when two fluids are present. In such a case, the pressure distribution is no longer equal to a constant or zero at the free interface. Taking the influence of an upper fluid upon the lower fluid into consideration, a series of fundamental solutions in closed forms arc presented in this paper.
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Key words:
- stratified fluids /
- singularity motion /
- analytical solution
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[1] Wehausen,J.V.and E.V.Laitone,Surface waves,Handbuch der Physik,9,Springer-Vcrlag(1960). [2] Lu,C.J.and Y.S.He,Unsteady theory of the hydrofoil of finite span,Acta MechanicaSinica,English Edi.1,2(1985). [3] Moran,J.P.and K.P.Kerney,On the small-perturbation theory of water-exit and entry,Developments in Mechanics,2,1(1965). [4] Lu,C.J.and Y.S.He,Fundamental solution of the rectangular vortex sheet moving with anarbitrary path when two fluids are present,Proc.of the 15th Midwestern Mechanics Conference,Ohio(1985). [5] 鲁传敬、何友声,计算非定常兴波问题新方法,水动力学研究与进展,2(1984). -
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