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Numerical computation of water waves with discontinuous vorticity

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NWWW01 - Nonlinear water waves

We consider progressive water waves with a piecewise constant vorticity distribution.
Both capillary-gravity waves and gravity waves of finite depth are considered.
This is a bifurcation problem of a complicated structure of solutions with many parameters.
It is hard to classify the structures of solutions mathematically.
We thus resort to a numerical method in order to see their bifurcating phenomena with systematic computations.
Another concern of ours is to see whether and when stagnation points appear.
The difficulties for numerical computations are that it is a free boundary problem and we need a formulation not to exclude stagnation points.
We will show our numerical results with various values of vorticity, depth of fluid and traveling speed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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