The physics of spontaneous parity-time symmetry breaking in the Kelvin-Helmholtz instability

We show that the dynamical system of an inviscid fluid with velocity shear admits parity-time (PT) symmetry, which provides a physical explanation of the well-known observation that the spectrum of the perturbation eigenmodes of the system is symmetric with respect to the real axis. It is found that the Kelvin-Helmholtz instability is triggered when and only when the PT symmetry is spontaneously broken. The analysis of PT symmetry also reveals that the relative phase between parallel velocity and pressure perturbations needs to be locked at π/2 when the instability is suppressed.