  The forcing of interstellar turbulence, driven mainly by supernova
explosions, is irrotational in nature, but the development of significant
amounts of vorticity and helicity, accompanied by large-scale dynamo action,
has been reported. Several earlier investigations examined vorticity production
in simpler systems; here all the relevant processes can be considered
simultaneously. We also investigate the mechanisms for the generation of net
helicity and large-scale flow in the system. We use a three-dimensional,
stratified, rotating and shearing local simulation domain of the size 1x1x2
kpc$^3$, forced with SN explosions occurring at the rate typical of the solar
neighbourhood in the Milky Way. In addition to the nominal simulation run with
realistic Milky Way parameters, we vary the rotation and shear rates, but keep
the absolute value of their ratio fixed. Reversing the sign of shear vs.
rotation allows us to separate the rotation- and shear-generated contributions.
As in earlier studies, we find the generation of significant amounts of
vorticity, with on average 65% of the kinetic energy being in the rotational
modes. The vorticity production can be related to the baroclinicity of the
flow, especially in the regions of hot, dilute clustered supernova bubbles. In
these regions, the vortex stretching acts as a sink of vorticity. The net
helicities produced by rotation and shear are of opposite signs for physically
motivated rotation laws, with the solar neighbourhood parameters resulting in
the near cancellation of the total net helicity. We also find the excitation of
oscillatory mean flows, the strength and oscillation period of which depend on
the Coriolis and shear parameters; we interpret these as signatures of the
anisotropic kinetic (AKA) effect. We use the method of moments to fit for the
turbulent transport coeffcients, and find $\alpha_{\rm AKA}$ values of the
order 3-5 km/s.
