A stability condition for planar flows not satisfying Blumen-Pedlosky's criterion

The non-linear stability of a class of two-dimensional-inviscid flows, not satisfying the Blumen-Pedlosky criterion, is proved. The result is based on the conservation of a proper functional of the disturbance that allows the determination of equivalent norms for which the considered planar flows ar e non-linearly stable. The related necessary condition for the instability is shown to hold for steady Rossby waves into a rectangular fluid domain. F inally, we match the present non-linear result with a previous study framed by a linear approach for a channelled flow.