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math-ph2022★ 21 cited
An efficient geometric method for incompressible hydrodynamics on the sphere
Paolo Cifani, Milo Viviani, Klas Modin
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hyd…
math-ph2021★ 19 cited
Canonical scale separation in two-dimensional incompressible hydrodynamics
Klas Modin, Milo Viviani
A two-dimensional inviscid incompressible fluid is governed by simple rules. Yet, to characterise its long-time behaviour is a knotty problem. The fluid evolves according to Euler'…
math-ph2020★ 1 cited
Integrability of point-vortex dynamics via symplectic reduction: a survey
Klas Modin, Milo Viviani
Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on 2-dimensional manifolds. Integrability results for few point-vortices on var…