He You-sheng, Lu Chuan-jing, Chen Xue-nong. Analytical Solutions of Singularities Moving with an Arbitrary Path when Two Fluids Are Present[J]. Applied Mathematics and Mechanics, 1991, 12(2): 119-134.
 Citation: He You-sheng, Lu Chuan-jing, Chen Xue-nong. Analytical Solutions of Singularities Moving with an Arbitrary Path when Two Fluids Are Present[J]. Applied Mathematics and Mechanics, 1991, 12(2): 119-134.

# Analytical Solutions of Singularities Moving with an Arbitrary Path when Two Fluids Are Present

• Publish Date: 1991-02-15
• 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.
•  [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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