Numerical Model of the Nonhydrostatic Equations

(0)12. 0

In this appendix, we discuss the details of the numerical model for system 3 (the Green-Naghdi equations with the horizontal rotation terms) alone, since both systems 1 & 2 may be obtained from system 3 by neglecting certain terms. The method of semi-Lagrangian discretization we use is based on Smolarkiewicz and Pudykiewicz [28], and the adaptation to the shallow-water system is on the lines of Nadiga et al.[13,29]. Finally, the solution of the elliptic equations is based on Smolarkiewicz and Margolin [14].

The momentum equation for system 3 is

where

with the same notation used in the text. The first line of () alone corresponds to system 1 and the first two terms of the second line of () are the extra terms in system 2. Using () in () and further simplifying, we have

where ,, and .