  The recently proposed low degree-of-freedom model of Moffat 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 Moffat and Kimura model accurately represents Euler's ideal fluid
equations of motion, we have shown the existence of finite-time singularity.
