The flow between two concentric cylinders, $V\left(r\right)$, is studied analytically and computationally for a fluid with stable axial density stratification. A sufficient condition for linear, inviscid instability is $d(V/r{)}^2/\mathrm{dr}<\mathrm{}0\mathrm{}$ (i.e., all anticyclonically sheared flows) rather than the Rayleigh condition for centrifugal instability, $d(\mathrm{Vr}{)}^2/\mathrm{dr}<\mathrm{}0\mathrm{}$. This implies a far wider range of instability than previously identified. The instability persists with finite viscosity and nonlinearity, leading to chaos and fully developed turbulence through a sequence of bifurcations. Laboratory tests are feasible and desirable.

• Received 4 May 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.5270