Abstract.
Within the Lagrangian framework we present an approach yielding some explicit solutions to the incompressible two-dimensional Euler equations, generalizing the celebrated Gerstner flow. The solutions so obtained, for which explicit formulas of each particle trajectory are provided, represent either flows in domains with a rigid boundary or free-surface flows for a fluid of infinite depth. For some of these solutions the trajectories are epitrochoids or hypotrochoids. Possibilities for obtaining further flows of this type are indicated.
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Communicated by D. H. Sattinger
W. A. S. supported in part by NSF grant DMS-0405066.
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Constantin, A., Strauss, W.A. Trochoidal Solutions to the Incompressible Two-Dimensional Euler Equations. J. Math. Fluid Mech. 12, 181–201 (2010). https://doi.org/10.1007/s00021-008-0281-2
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DOI: https://doi.org/10.1007/s00021-008-0281-2