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

Abstract

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, reducedgravity 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 coastalcurrent instabilities. IntroductionA substantial portion of the ocean's energy is contained in the so-called mesoscale activity, the internal weather of the sea. These motions, with length scales of the order of the first baroclinic radius of deformation (20-200 km), are mostly comprosed of jets and vortices [Robinson, 1983]. Their length scale implicates geostrophy, and, consequently, their relative high velocities are accompanied by substantial vertical displacements of density surfaces, causing on numerous occasions their outcrop through the surface. Examples are the north wall of the Gulf Stream, the periphery of its detached rings, the offshore edge of coastal intrusions, and upwelling fronts. We shall use here the word "front" to describe the surface outcropping of a pycnocline or, in the context of a layered model, the surfacing of a density interface. Indeed, such outcropping causes important horizontal density gradients along the surface and corresponds to a frontal zone.Since geostrophy places a high degree of relation between horizontal density gradients and velocities (via the thermalwind balance), fronts are accompanied by flow fields that are highly sheared in the horizontal a...

Analytical Solutions for Circular Stratified Eddies of the Reduced-Gravity Shallow-Water Equations

“…In particular, one remarkable peculiarity of the nonlinear, reduced-gravity shallow-water equations on an f plane is that they can be solved analytically in special cases of geophysical interest (see, e.g., Ball 1963;Thacker 1981;Young 1986;Cushman-Roisin 1987;Rogers 1989;Rubino et al 1998;Rubino and Dotsenko 2006). Such a characteristic has a particular relevance in oceanic sciences: apart from their intrinsic value and fascinations, analytical solutions of nonlinear equations referring to the dynamics of geophysical motions can help to evidence fundamental aspects inherent in the dynamics of observed flow features that may be difficult to unravel when their whole complexity is addressed (Esenkov and Cushman-Roisin 1999;Rubino and Dotsenko 2006). Moreover, such solutions can be used for assessing the performance of numerical models (see, e.g., Sun et al 1993;Esenkov and Cushman-Roisin 1999;Rubino et al 2002).…”

“…Such a characteristic has a particular relevance in oceanic sciences: apart from their intrinsic value and fascinations, analytical solutions of nonlinear equations referring to the dynamics of geophysical motions can help to evidence fundamental aspects inherent in the dynamics of observed flow features that may be difficult to unravel when their whole complexity is addressed (Esenkov and Cushman-Roisin 1999;Rubino and Dotsenko 2006). Moreover, such solutions can be used for assessing the performance of numerical models (see, e.g., Sun et al 1993;Esenkov and Cushman-Roisin 1999;Rubino et al 2002). It is thus not surprising that, in the last decades, analytical solutions of the nonlinear reduced-gravity shallow-water equations referring to geophysical rotating vortices have been presented in different investigations.…”

The Rhine Outflow Plume Studied by the Analysis of Synthetic Aperture Radar Data and Numerical Simulations

“…One could thus consider threedimensional primitive equation models as the most adequate tools for the simulation of these fronts. However, a detailed description of the entire complexity of the surface frontal dynamics in a river outflow region is largely inhibited by its often unsustainedly high computational effort (O'Donnell 1993;Esenkov and Cushman-Roisin 1999), as well as by the sensitivity of the obtained solutions to the parametrizations adopted for taking into account turbulent processes (Ruddick et al 1995). For these reasons, more efficient ''process modeling'' strategies have been developed in the last three decades, which are still considered among the most valid tools for the description of oceanic flow features including frontal processes.…”

The Stratified Pulson

“…Moreover, such solutions can constitute an excellent basis for testing the performance of numerical models. This is especially true in the simulation of stratified surface as well as intermediate lenslike vortices, where one is faced on one hand with the complexity of implementing accurate techniques for the simulation of movable lateral boundaries needed for the description of the vortex expansions, contractions, and propagation and, on the other hand, with the difficulty of adequately resolving observed horizontal and vertical stratification (see, e.g., Sun et al 1993;Esenkov and Cushman-Roisin 1999).…”