| Abstract: |
| In this talk, I will present a global bifurcation result for doubly periodic gravity-capillary water waves with vorticity. Specifically, I consider the class of Beltrami flows, in which the velocity and vorticity fields are collinear. This structure allows us to reformulate the governing equations as a perturbation of the identity by a compact operator, enabling the application of analytic global bifurcation theory to obtain solutions along a global continuum emerging from the laminar flow. The main challenge is the presence of a two-dimensional kernel at the bifurcation point, and I will explain how this can be handled by treating the parameterisation of the local bifurcation curve as a new bifurcation parameter.
This is joint work with Giang To and Erik Wahl\`{e}n (both Lund University). |
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