Barotropic-Baroclinic Time Splitting for Ocean Circulation Modeling

Abstract

Numerical models of ocean circulation admit motions varying on a wide range of time scales. These motions include fast external gravity waves, which are approximately independent of depth, and slower internal motions which are fully three-dimensional. Explicit time discretizations are impractical for these systems, due to the short timesteps dictated by the fast waves. A commonly used alternative is to confine the fast waves to a two-dimensional system, via vertical averaging, and then to compute the remaining motions explicitly with a long time step. However, this procedure can lead to numerical instability if the latter system admits sufficiently large residual fast motions due to an inexact splitting. In this paper we modify a method developed by R. Bleck and L. T. Smith (J. Geophys. Res. C95,3273, 1990) in order to obtain a more precise splitting into fast and slow subsystems. In the vertically averaged momentum equation, we use the exact vertical average of the horizontal pressure gradient in place of the approximation used inop cit.We then apply natural time discretizations and show that the modified splitting produces considerable improvements in stability.