Conditional stability conditions for a semi-implicit PE barotropic model

"Difficulties encountered with the semi-implicit version of the Shuman-Hovermale model (Gerrity 1973) when orography was incorporated suggested the possibility that linear computational instability might be associated with the large variations of the specific volume on a a-coordinate surface in the presence of mountains. Some numerical experiments with a freesurface PE barotropic model with orography were undertaken in order to shed light on the subject. In this note, a stability analysis of the barotropic model is presented which supports the general stability of the semi-implicit method but does indicate the existence of a conditional stability requirement; viz., the "deviation" phase velocity-must not be large compared to the "mean" phase velocity"--Introduction. J.P. Gerrity. "June 1974." Includes bibliographical references (page 7).