An Ocean Circulation Model Based on Operator-Splitting, Hamiltonian Brackets, and the Inclusion of Sound Waves

Abstract

Abstract This paper offers a simple, entirely prognostic, ocean circulation model based on the separation of the complete dynamics, including sound waves, into elementary Poisson brackets. For example, one bracket corresponds to the propagation of sound waves in a single direction. Other brackets correspond to the rotation of the velocity vector by individual components of the vorticity and to the action of buoyancy force. The dynamics is solved by Strang splitting of the brackets. Key features of the method are the assumption that the sound waves propagate exactly one grid distance in a time step and the use of Riemann invariants to solve the sound-wave dynamics exactly. In these features the method resembles the lattice Boltzmann method, but the flexibility of more conventional methods is retained. As in the lattice Boltzmann method, very short time steps are required to prevent unrealistically strong coupling between the sound waves and the slow hydrodynamic motions of primary interest. However, the disadvantage of small time steps is more than compensated by the model’s extreme simplicity, even in the presence of very complicated boundaries, and by its massively parallel form. Numerical tests and examples illustrate the practicality of the method.