Symmetric Instability without Symmetry

Abstract

When a basic flow with linear or axial symmetry has a region of negative potential vonicity (hereafter PV), such a disturbance with the same symmetry as the basic flow grows that converts the negative PV of the region into non-negative PV. This is the so-called symmetric instability.
In this note, the following is shown in a nondissipative adiabatic system. Irrespective of the symmetry, disturbances grow in the region of negative PV. That is, irrespective of the symmetry, a flow with negative PV is unstable. This statement is based on the conservation law of absolute circulation around a material closed curve on the isentropic surface.