29.2 stream_function

Option stream_function enables the time honored standard approach which eliminates surface pressure from the momentum equations by vertically integrating, taking the curl, and assuming that vertical velocity vanishes at the ocean surface which is taken at z=0. This rigid lid approach was developed by Bryan (1969) and has remained the choice of numerous ocean modelers for almost 30 years. However, for the reasons mentioned in Section 29.1, the rigid lid is being displaced by the more physically complete and computationally efficient (with regard to parallelism) free surface approaches. This section discusses the computational implementation of the rigid lid. The theoretical formulation is given in Bryan (1969).

Boundary conditions for the rigid lid barotropic streamfunction are Dirichlet, which necessitate solving island equations as given in Section 29.2.4. Artificially setting the flow between land masses to zero may be implemented, as described in Section 29.2.6. Changes^29.2 to the coefficient matrices and in the handling of islands in the elliptic solvers have resulted in faster convergence rates than in MOM 1. The external mode velocities given by the stream function approach are guaranteed to be divergence free even if the solution for change in stream function $\Delta \psi$ is not accurate. The accuracy of the solution for $\Delta \psi$ is governed by ``tolrsf'' which is input through namelist. Typically, the value is 10⁸ cm³/sec.