BAROTROPIC-BAROCLINIC TIME SPLITTING FOR OCEAN CIRCULATION MODELING

Numerical models of ocean circulation admit motions varying on a wide range of time scales. These motions include fast external gravity wave s, which are approximately independent of depth, and slower internal m otions which are fully three-dimensional. Explicit time discretization s are impractical for these systems, due to the short timesteps dictat ed by the fast waves. A commonly used alternative is to confine the fa st waves to a two-dimensional system, via vertical averaging, and then to compute the remaining motions explicitly with a long time step. Ho wever, this procedure can lead to numerical instability if the latter system admits sufficiently large residual fast motions due to an inexa ct splitting. In this paper we modify a method developed by R. Bleck a nd L. T. Smith (J. Geophys. Res. C 95. 3273, 1990) in order to obtain a more precise splitting into fast and slow subsystems. In the vertica lly averaged momentum equation, we use the exact vertical average of t he horizontal pressure gradient in place of the approximation used in op cit. We then apply natural time discretizations and show that the m odified splitting produces considerable improvements in stability. (C) 1997 Academic Press.