Green functions with pulsating sources in a two-layer fluid of finite depth |
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Authors: | D O Manyanga Wen-yang Duan |
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Institution: | College of Shipbuilding,Harbin Engineering University,Harbin 150001,China |
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Abstract: | The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with
the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface.
This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.
The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried
out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of
singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of
equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations
are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can
be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for
each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal
wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible
and the flow is irrotational. |
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Keywords: | Green function two-layer fluid three dimensions singularities method |
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