Absolute Instability Induced by Dissipation

Abstract

A two-layer quasigeostrophic model is used to investigate whether dissipation can induce absolute instability in otherwise convectively unstable or stable background states. It is shown that dissipation of either temperature or lower-layer potential vorticity can cause absolute instabilities over a wide range of parameter values and over a wide range of positive lower-layer velocities (for positive vertical shear). It is further shown that these induced absolute instabilities can be manifested as local instabilities with similar properties. Compared to the previously known absolute instabilities, the induced absolute instabilities are characterized by larger scales, weaker absolute growth rates, and substantially weaker vertical phase tilt (typical values for subtropical states are zonal wavenumber 1?3, absolute growth rate 80?100 days, and period 7?10 days). The analysis of absolute instabilities, including the case of multiple absolute instabilities, is reviewed in an appendix. Because the dispersion relation of the two-layer model can be written as a polynomial in both wavenumber and frequency, all possible saddle points and poles of the dispersion relation can be determined directly. An unusual feature of induced absolute instabilities is that the absolute growth rate can change discontinuously for small changes in the basic-state parameters. The occurrence of a discontinuity in the secondary instability is not limited to the two-layer model but is a general possibility in any system involving multiple absolute instabilities. Depending on the location of the discontinuity relative to the packet peak, a purely local analysis, as used in many numerical techniques, would extrapolate the secondary absolute instability to incorrect regions of parameter space or fail to detect the secondary absolute instability altogether. An efficient procedure for identifying absolute instabilities that accounts for these issues is developed and applied to the two-layer model.