Eur. Phys. J. Plus (2013) 128: 18
https://doi.org/10.1140/epjp/i2013-13018-0

Regular Article

Stability of barotropic geostrophic flows revisited with some applications

¹ Dipartimento di Fisica, Università di Trieste, Trieste, Italy
² Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Trieste, Italy
³ CNR-ISAC, Roma, Italy

^* e-mail: fulvio_crisciani@alice.it

Received: 25 October 2012
Revised: 25 January 2013
Accepted: 28 January 2013
Published online: 19 February 2013

Abstract

The stability of inertial barotropic flows with a negative derivative of potential vorticity with respect to the stream function is investigated. A method developed by Pedlosky is extended to the above case and compared with classical results by Arnold. If such derivative is a constant, the stability criterion is valid also in the nonlinear regime. On the other hand, in the linear framework the obtained result is included in the criterion obtained by the standard normal mode analysis. Some applications to the East-West symmetry of the flow as well to the circulation over topography are considered.