Eur. Phys. J. D 13, 393-399 (2001)
https://doi.org/10.1007/s100530170258

On the stability of the inertial circulation in the 11/2-layer, quasi-geostrophic model

Istituto Talassografico del CNR, Viale Romolo Gessi 2, 34123 Trieste, Italy

Corresponding author: ^a fulcri@itt.ts.cnr.it

Received: 8 June 2000
Revised: 18 September 2000
Published online: 15 March 2001

Abstract

The effect of the time-dependent interface, separating an inertial quasi-geostrophic upper fluid layer from the quiescent abyss, on the non-linear stability of a steady circulation that takes place in this layer is explored. The analysis resorts to the method of Arnol'd's invariant resulting in a conditional stability criterion, which proves the stabilizing effect of the interface with respect to the single-layer case. The uniqueness of the stable basic flow field follows. Finally, non-linear and linear analyses are compared in the special case of a channeled flow with a fluctuating interface, the latter leading to an unconditional stability statement, whose meaning is clarified by resorting to the previously obtained nonlinear criterion.