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math-ph2020
The Godbillon-Vey Invariant as Topological Vorticity Compression and Obstruction to Steady Flow in Ideal Fluids
Thomas Machon
If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields the Godbillon-Vey (GV) invaria…
math-ph2020
The Godbillon-Vey Invariant as a Restricted Casimir of Three-dimensional Ideal Fluids
Thomas Machon
We show the Godbillon-Vey invariant arises as a `restricted Casimir' invariant for three-dimensional ideal fluids associated to a foliation. We compare to a finite-dimensional syst…