Spurious instabilities of long planetary waves in a two-and-a-half layer model subtropical gyre ocean with a wind-driven steady circulation

Abstract

In a number of flows that support coupled free-waves, instability results when free-wave dispersion relations calculated without the coupling cross or approach one another. The propagation of long planetary wave perturbations of a two-and-a-half layer model subtropical gyre is one such oceanographically important instance. This note points out that, for a baroclinically unstable two-and-a-half layer model subtropical gyre, numerically aliased long wave dispersion relation plots display extra crossings that are artifacts of the discretization, and these may lead both to spurious numerical instabilities and to numerical misrepresentation of actual instabilities. Paradoxically, the numerical instability may in some instances manifest itself more strongly as the numerical resolution is improved. The aliasing mechanism may be related to the zone of small scale activity found in the southwestern corner of a time dependent model subtropical gyre in the numerical perturbation experiments of (Dewar, W., Huang, R., 2001. Adjustment of the ventilated thermocline. J. Phys. Oceanogr. 13, 293–309). Similar multilayer models are often discussed in the literature, so that the results may be widely useful.