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 are presented in this paper.
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Dedicated to the Tenth Anniversary and One Hundred Numbers of AMM (II)
The Project supported by National Natural Science Foundation of China
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You-sheng, H., Chuan-jing, L. & Xue-nong, C. Analytical solutions of singularities moving with an arbitrary path when two fluids are present. Appl Math Mech 12, 131–148 (1991). https://doi.org/10.1007/BF02016532
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DOI: https://doi.org/10.1007/BF02016532