2004 Fiscal Year Final Research Report Summary
Numerical approach for bifurcation of nonlinear problem
| Project/Area Number |
14540140
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Japan Women's University |
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Principal Investigator |
SHOJI Mayumi Japan Women's University, Fac.of Science, Professor, 理学部, 教授 (10216161)
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| Project Period (FY) |
2002 – 2004
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| Keywords | water wave / bifurcation / rotational flow |
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| Research Abstract |
It attempted to take up some problems that there was a loose end in the conventional research about the bifurcation of water waves once again. As a result in this research, it won a result like the following in case of numerical simulation of the rotational flow.
Our aim is computing bifurcation branches for changing vorticity distribution and classifying extreme wave profiles along with our conventional research results. It used the way according to Zeidler to compute a free boundary problem with vorticity. In the process of proceeding with the numerical experiment, this way showed that it wasn't sometimes possible to compute when a closed eddy occurs. Until the present, it understands the existence might be in the case of constant vorticity. However it is a problem to be confirmed whether there occur a closed eddy in the case of general vorticity distribution. It did a numerical simulation by a finite difference method and it got some results. As for the depth, it handled only a finit
… More
e case.
Our results in the research are as follows. Hereinafter, we considered the case where the vorticity function is positive (or negative) everywhere and decays with the depth. When the surface tension works, however it gives vorticity distribution, all the extreme wave profiles are overhanging type or overlapped type, namely smooth boundary. For gravity waves, when the vorticity function decays with the water depth, it becomes the extreme wave profile has corner or cusp. On the other hand, in the case of the constant vorticity of gravity waves, there appears an overhanging type of waves on the way to the extreme wave, which has a corner at last. According to our experiments, it is only in the case of the constant vorticity to be seen such overhanging type of gravity waves. It is remarkable phenomenon for gravity waves and it needs to be more reviewed by it in the future.
We presented the above results in "Taiwan-Japan Joint Conference on Nonlinear Analysis and Applied Mathematics" at Institute of Mathematics Academia Sinica of Taipei. It plans to gather as the paper after arranging for a few pieces of numerical data. Less
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Research Products
(2 results)
