Symmetric and nonsymmetric Holmboe instabilities in an inviscid flow

Using linear stability analysis we studied the effect of displacing a thin density interface with respect to the center of the shear layer on the stab ility of an inviscid, stably stratified, parallel flow. When no interface d isplacement is present and the how is unbounded, pure Holmboe instabilities exist at all bulk Richardson numbers and are the most unstable instabiliti es for values of the bulk Richardson number greater than 0.046. When the in terface displacement is nonzero the two modes of a Holmboe instability spli t into a stronger and a weaker mode. As the height of the vertical domain d ecreases the roles of the two modes switch with the originally weaker mode becoming the stronger mode and vice versa. The importance of including the height of the vertical domain in the stability analysis was illustrated by comparing theoretical results with the field data of Yoshida ct al. [Yoshid a, Ohtani, Nishida, and Linden, in Physical Processes in Lakes and Oceans, edited by J. Imberger (American Geophysical Union, Washington, DC, 1998), p p. 389-400]. The assumption that the instabilities are initially two-dimens ional is examined. When the flow is unbounded, both symmetric and nonsymmet ric Holmboe instabilities are initially two-dimensional. When boundaries ar e included, the two-dimensional assumption is valid except when the total v ertical domain is small in which case three-dimensional primary instabiliti es are possible. (C) 1999 American Institute of Physics. [S1070-6631(99)011 06-X].