We derive and analyze several low dimensional Hamiltonian normal
forms describing system symmetry breaking in ideal hydrodynamics.
The equations depend on two parameters (
,
),
where
is the strength of a system symmetry breaking
perturbation and
is a detuning parameter. In many cases
the resulting equations are completely integrable and have an
interesting Hamiltonian structure. Our work is motivated by
three-dimensional instabilities of rotating columnar fluid flows
with circular streamlines (such as the Burger vortex) subjected
to precession, elliptical distortion or off-center displacement.
