On the Theory of Symmetric Instability of Time-Periodic Flows with a Complete Account for the Coriolis Force

The symmetric (inertial) parametric instability of time-periodic flows with a linear velocity profile has been investigated, with a complete account for the Coriolis force in the problem. The possibility of instability is shown at velocity shears smaller than those indicated by the criterion of inertial stability of a stationary flow with the same velocity amplitude. The most significant results are obtained in the limit of weak density stratification of the medium, which is characteristic of well-mixed vertically convective layers of the atmosphere, in the deep layers of the ocean, and can also be directly related to a laboratory experiment.