  We study the stability of two-dimensional inviscid flows in an annulus
between two porous cylinders with respect to three-dimensional perturbations.
The basic flow is irrotational, and both radial and azimuthal components of the
velocity are non-zero. The direction of the radial flow can be from the inner
cylinder to the outer one (the diverging flow) or from the outer cylinder to
the inner one (the converging flow). It had been shown earlier in Ref.
\cite{IM2013a} that, independent of the direction of the radial flow, the basic
flow can be unstable to small two-dimensional perturbations. In the present
paper, we prove first that purely radial flow is stable and that flows with
both radial and azimuthal components are always stable to axisymmetric
perturbations. Then we show that both the diverging and converging flows are
unstable with respect to non-axisymmetric three-dimensional perturbations
provided that the ratio of the azimuthal component of the velocity to the
radial one is sufficiently large. Neutral curves in the space of parameters of
the problem are computed and it is demonstrated that for any ratio of the radii
of the cylinders, the most unstable modes (corresponding to the smallest ratio
of the azimuthal velocity to the radial one) are the two-dimensional ones. We
also consider the corresponding viscous stability problem and construct an
asymptotic expansion of its solutions for large radial Reynolds numbers. We
compute the first-order viscous correction to inviscid eigenvalues and show
that the asymptotic results give a good approximation to the viscous
eigenvalues even for moderate values of radial Reynolds number, which indicates
that the instability may be observed in real flows.
