How do CPT-like symmetries shape the stability of geophysical flows?

Abstract

We examine the role discrete symmetries, timereversal and mirror symmetries, play in the context of geophysical waves and instabilities. By looking at three special cases from the two-layer quasigeostrophic model as well as developing a general framework for translating real-space transformations to Fourier-space we are able to: 1) show that baroclinic instability is an example of spontaneous paritytime symmetry breaking; 2) show that pure parity symmetry for a fluid system is exactly analogous to charge-conjugation-parity symmetry in a condensed matter system; and 3) show that when a pure parity symmetry is broken, this is associated with the suppression of wave propagation. Further, in the latter case, instability can arise without a corresponding symmetry breaking. This study highlights the role of symmetry breaking behind the dynamics of geophysical waves and instabilities.