|Numerical mass conservation in a free-surface sigma coordinate marine model with mode splitting|
Deleersnijder, E. (1993). Numerical mass conservation in a free-surface sigma coordinate marine model with mode splitting. J. Mar. Syst. 4: 365-370
In: Journal of Marine Systems. Elsevier: Tokyo; Oxford; New York; Amsterdam. ISSN 0924-7963, more
Dynamical oceanography; Hydrodynamic equations; Ocean circulation; Transport processes; Marine
When the mode splitting technique is used the variables playing a role in the mass conservation equation are computed with different frequencies, since two time steps are utilized. The three-dimensional velocity field advecting the scalar quantities must however be divergence free--in the time stepping of the scalar quantities. A simple method aiming at enforcing this condition is outlined in the case of a free-surface sigma coordinate model using a "forward time stepping." This technique consists in using the sum of the baroclinic transport at the old time step and the average of the barotropic transport over the baroclinic time increment. In the Appendix, one suggest another method, less accurte but capable of being used with any kind of time stepping.