A note on the stability of a family of space-periodic Beltrami flows

The linear stability of the ‘ABC’ flows u = ( A sin z + C cos y, B sin x + A cos z, C sin y + B cos x ) is investigated numerically, in the presence of dissipation, for the case where the perturbation has the same 2π-periodicity as the basic flow. Above a critical Reynolds number, the flows are in general found to be unstable, with a growth time that becomes comparable to the dynamical timescale of the flow as the Reynolds number becomes large. The fastest-growing disturbance field is spatially intermittent, and reaches its peak intensity in features which are localized within or at the edge of regions where the undisturbed flow is chaotic, as occurs in the corresponding MHD problem.