Rui Duarte

In a barotropic model of an oceanic channel, bounded to the north by a straight coast indented by a Gaussian cape, the evolution of a coastal jet is studied numerically. In the absence of the cape, the barotropic instability of the jet is determined. In the presence of the cape, a regular row of meanders develops downstream of this feature, and becomes stationary for a particular range of parameters. The relevant parameters are the velocity and width of the jet, size of the cape, and beta effect. The formation of meanders occurs first via the instability of the jet, then via the generation of vorticity anomalies at the cape, which are advected both downstream by the flow and offshore by the radiation of Rossby waves. Once the meanders are established, they remain stationary features if the propagation velocity of the meanders (due to the dipolar effect at the coast) opposes the jet velocity and the phase speed of the wave on the vorticity front. Finally, a steady state of a regular row of meanders is also obtained via a matrix method and is similar to that obtained in the time-dependent case.

This paper addresses the instability of a two-layer coastal current in a quasigeostrophic model; the potential vorticity (PV) structure of this current consists in two uniform cores, located at different depths, with finite width and horizontally shifted. This shift allows both barotropic and baroclinic instability for this current. The PV cores can be like-signed or opposite-signed, leading to their vertical alignment or to their hetonic coupling. These two aspects are novel compared to previous studies. For narrow vorticity cores, short waves dominate, associated with barotropic instability; for wider cores, longer waves are more unstable and are associated with baroclinic processes. Numerical experiments were performed on the $f$−plane with a finite-difference model. When both cores have like-signed PV, trapped instability develops during the nonlinear evolution: vertical alignment of the structures is observed. For narrow cores, short wave breaking occurs close to the coast; for wider cores, substantial turbulence results from the entrainment of ambient fluid into the coastal jet. When the two cores have opposite-signed PV, the nonlinear regimes range from short wave breaking to the ejection of dipoles or tripoles, via a regime of dipole oscillation near the wall. The Fourier analysis of the perturbed flow is appropriate to distinguish the regimes of short wave breaking, of dipole formation, and of turbulence, but not the differences between regimes involving only vortex pairs. To explain more precisely the regimes where two vortices (and their wall images) interact, a point vortex model is appropriate.