Modeling of two‐layer eddies and coastal flows with a particle method

Abstract

An existing particle‐in‐cell (PIC) numerical method developed for the study of two‐layer mesoscale motions with outcropping pycnocline is applied to lens‐like anticyclonic vortices and buoyant coastal currents. From a first series of experiments investigating the evolution of an initially elongated lens‐like anticyclone, it is found that motions induced in the lower layer act only to increase the rotation of the vortex structure and do not appear to affect the process of eccentricity reduction (partial axisymmetrization). Eccentricity reduction, if any, produces a final vortex of aspect ratio between 1.8 and 1.9, a value that is very close to the stability threshold of large, reduced‐gravity lenses. A second series of experiments devoted to vortex mergers determines how the maximal separation distance for which two circular anticyclonic lenses merge spontaneously varies with vortex size (ratio of lens radius to deformation radius) and stratification (ratio of lens central thickness to ocean depth). A third series of experiments considers the interaction of a lens vortex in the upper layer with a potential‐vorticity anomaly in the lower layer. “Second‐hand” relative vorticity, generated in the lower layer under the action of vertical stretching induced by the movement of the upper‐layer vortex, interacts with “first‐hand” relative vorticity, created by the existing potential‐vorticity, to create effects similar to those predicted by studies of two‐layer point vortices (hetons). Finally, the PIC method is generalized to simulate the finite‐amplitude instability of a buoyant geostrophic/hydrostatic intrusion flowing along a vertical coastal wall. Those results, however, are reported here more as a demonstration on how the PIC method can be extended to include coastal boundaries than as a thorough investigation of coastal‐current instabilities.