Reply to a note by T. G. Shepherd

Summary In a recent note by Shepherd it is claimed that the main conclusions discussed in a paper by Petroniet al. about certain instability mechanisms for steady equivalent barotropic flows are incorrect and, although no criticism is made regarding the analytical treatment, two counterexamples are presented to support this thesis. In addition to this it is asserted that the envisaged necessity for energy and enstrophy to be transferred in both spatial directions in a normal-mode instability is ?extremely well known?. Here we demonstrate that Shepherd's conclusions are without foundation and confirm the validity and originality of Petroniet al. results by showing that:a) the first counterexample describes a situation that is in fact provided for by Petroniet al.'s analysis;b) the second counterexample is not dynamically realizable and, even if it were, the related conclusions would not apply to flows defined in doubly periodic or bounded domains such as those considered by Petroniet al.; c) the mechanism cited above is not known at all in the specific context dealt with by Petroniet al. We emphasize this by pointing out that for steady equivalent barotropic flows the range of parameters for which such an instability mechanism is allowed complements exactly the range for which the steady states are stable according to Benziet al.