  While classical or quantum interacting liquids become turbulent under
sufficiently strong driving, it is not obvious what flow pattern an ideal
quantum gas develops under similar conditions. Unlike classical noninteracting
particles which exhibit rather trivial flow, ideal fermions have to satisfy the
exclusion principle, which acts as a form of collective repulsion. We thus
study the flow of an ideal Fermi gas as it is driven out of a narrow orifice of
width comparable to the Fermi wavelength, employing both a microcanonical
approach to transport, and solving a Lindblad equation for Markovian driving
leads. Both methods are in good agreement and predict an outflowing current
density with a complex microscopic pattern of vorticity in the steady state.
Applying a bias of the order of the chemical potential results in a short-range
correlated antiferromagnetic vorticity pattern, corresponding to local moments
of the order of a tenth of a magneton, $e\hbar/2m$, if the fermions are
charged. The latter may be detectable by magnetosensitive spectroscopy in
strongly driven cold gases (atoms) or clean electronic nanostructures
(electrons).
