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- W4386002805 abstract "The recently proposed low degree-of-freedom model of Moffatt and Kimura [1], [2] for describing the approach to finite-time singularity of the incompressible Euler fluid equations is investigated. The model assumes an initial finite-energy configuration of two vortex rings placed symmetrically on two tilted planes. The Hamiltonian structure of the inviscid limit of the model is obtained. The associated noncanonical Poisson bracket [3] and two invariants, one that serves as the Hamiltonian and the other a Casimir invariant, are discovered. It is shown that the system is integrable with a solution that lies on the intersection for the two invariants, just as for the free rigid body of mechanics whose solution lies on the intersection of the kinetic energy and angular momentum surfaces. Also, a direct quadrature is given and used to demonstrate the Leray form for finite-time singularity in the model. To the extent the Moffatt and Kimura model accurately represents Euler's ideal fluid equations of motion, we have shown the existence of finite-time singularity." @default.
- W4386002805 created "2023-08-20" @default.
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- W4386002805 date "2023-10-01" @default.
- W4386002805 modified "2023-10-17" @default.
- W4386002805 title "A Hamiltonian description of finite-time singularity in Euler's fluid equations" @default.
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- W4386002805 doi "https://doi.org/10.1016/j.physleta.2023.129078" @default.
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