How to Overcome Numerical Instability when the Density Jump Between Layers is Constant

Abstract

It has been observed in oceanic modelling that numerical instability is caused
when the density jump between layers is constant. This instability is usually
overcome by using variable density jumps, according to McNider & O'Brien
(1973). In decomposing the vertical modes of the linearized model equation, it is shown that the eigenvectors of the layered system may introduce an anomalous fast mode if the parameærs are not adequaæly chosen.