Lattice Boltzmann solutions of the three-dimensional planetary geostrophic equations

We use the lattice Boltzmann method as the basis for a three-dimensional, numerical ocean circulationmodel in a rectangularbasin. The fundamental dynamical variables are the populationsof massand buoyancy-particleswith prescribed discrete velocities. The particles obey collision rules that correspond,on the macroscopic scale, to planetary geostrophicdynamics.The advantagesof the model are simplicity, stability, and massively parallel construction. By the special nature of its construction, the lattice Boltzmann model resolves upwelling boundary layers and unsteady convection. Solutions of the model show many of the features predicted by ocean circulation theories.