Could a Pile of Slippery Sacks Behave Like an Ocean?

Abstract

A method for simulating fluid motions that shows promise for application to the oceans is explored. Incompressible inviscid fluids with free surfaces are represented as piles of slippery sacks. A system of ordinary differential equations governs the motions of the sacks, and this system is solved numerically in order to simulate a nonlinear deformation, internal and external gravity waves, and Rossby waves. The simulations are compared to analytic and finite-difference solutions, and the former converge to the latter as the sizes of the sacks are decreased. The slippery-sack method appears to be well suited to ocean modeling for the following reasons: 1) it perfectly conserves a fluid's distributions of density and tracers; 2) unlike existing isopycnic models the slippery-sack method is capable of representing a continuum of fluid densities and vertically resolving neutral regions; 3) the inclusion of continuous topography adds no numerical complexity to the slippery-sack method; 4) the slippery-sack method conserves energy in the limit as the time step approaches zero; and 5) the slippery-sack method is computationally efficient.