A particle-in-cell method for the solution of two-layer shallow-water equations

A particle-in-cell (PIC) numerical method developed for the study of shallo w-water dynamics, when the moving fluid layer is laterally confined by the intersection of its top and bottom surfaces, is described. The effect of am bient rotation is included for application to geophysical fluids, particula rly open-ocean buoyant vortices in which the underlying density interface o utcrops to the surface around the rim of the vortex. Extensions to include the dynamical effect of a second moving layer (baroclinicity) and the prese nce of a lateral rigid boundary (sidewall) are also described. Although the method was developed for oceanographic investigations, applications to oth er fluid mechanics problems would be straightforward. Copyright (C) 2000 Jo hn Wiley & Sons, Ltd.