Abstract:

The alternative leapfrog scheme is an efficient and non-dissipative scheme developed for liner shallow water equa-
tions in  z-coordinate. In this study, the scheme is used for non-liner equations in  σ-coordinate. The application to
two-dimensional barotropic equations in  the Princeton Ocean Model (POM) is numerically investigated. First, the numerical
results of one-dimensional wave are given, and the development of non-linear wave is described in details to show its
non-linear character. The results also show that the alternative leapfrog scheme has the advantage of its numerically conserved
property and computational stability, which are better than those using the conventional leapfrog scheme. Second, the Coriolis
term is numerically dealt with in the two-dimensional barotropic equations in order to match the alternative leapfrog scheme,
and the numerical results are investigated in terms of the external mode of POM. The results show that with the alternative
leapfrog scheme, the external mode of POM has numerical advantages of high computational efficiency twice as much as the
original scheme, simplicity without Assenlin filter, and higher numerical conservation than that in POM due to Assenlin filter’s
damping.

Key words: alternative leapfrog, σ-coordinate, shallow water equation, barotropic equation, Princeton Ocean Model (POM)