Secondary Bifurcation and Change of Type for Three Dimensional Standing Waves in Shallow Water.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This is an analysis of three dimensional surface waves which occur in a vessel of rectangular cross section and finite depth. The linearized problem has double eigenvalues for particular combinations of the parameters. It is shown that eight solution branches of finite amplitude are emitted by the double eigenvalues. Splitting of the double eigenvalues results in a secondary bifurcation. The direction of the emitted branches for the multiple and secondary bifurcation changes with the depth of the fluid. Finally it is shown that the formal solutions obtained are not uniformly valid and an additional expansion in the region of non-uniformity shows that the wave field changes type. One possibility in this region is a field of three dimensional cnoidal standing waves.
- Numerical Mathematics
- Fluid Mechanics