## A geometrical study of 3D incompressible Euler flows with Clebsch potentials

*Koji Ohkitani*, Department of Applied Mathematics, University of Sheffield

We consider a special class of flows which have Clebsch
potentials to explore possibility of blow up of the incompressible 3D
Euler equations. This is perhaps geometrically the simplest, but
nevertheless nontrivial vortex. After briefly reviewing what
Clebsch has done, we introduce a criterion for geometric
non-degeneracy, which should be satisfied for a possible blowup. Some
preliminary results of numerical simulations will be presented. We
will consider two kinds of initial conditions: (1) a simple choice of
Clebsch potentials, and (2) Kida's high symmetric flow. For (1), we test
the above-mentioned criterion for the early stage evolution. For (2),
we derive the expressions for initial Clebsch potentials and observe
their evolution.

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