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We examine the role discrete symmetries, time-reversal and mirror symmetries,play in the context of geophysical waves and instabilities. By looking at threespecial cases from the two-layer quasi-geostrophic model as well as developinga general framework for translating real-space transformations to Fourier-spacewe are able to: 1) show that baroclinic instability is an example ofspontaneous parity-time symmetry breaking; 2) show that pure parity symmetryfor a fluid system is exactly analogous to charge-conjugation-parity symmetryin a condensed matter system; and 3) show that when a pure parity symmetry isbroken, this is associated with the suppression of wave propagation. Further,in the latter case, instability can arise without a corresponding symmetrybreaking. This study highlights the role of symmetry breaking behind thedynamics of geophysical waves and instabilities.

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