Inertial instability of the time-periodic Kolmogorov flow in a rotating fluid with the full account of the Coriolis force

Abstract

The inertial parametric instability of a time-dependent spatially periodic flow (Kolmogorov flow) of a rotating stratified Boussinesq fluid is studied, taking fully into account the Coriolis force in the problem and with the possibility that the flow has an arbitrary orientation in the horizontal plane. The existence of instability is shown for velocity shears less than those indicated by the criterion of inertial stability of a steady flow with the same spatial period and velocity amplitude. In particular, the instability estimates are obtained for weakly stratified geophysical media, for example for the deep layers of the ocean, and it is suggested that the possible applications of the theory can also be directly related to a laboratory experiment. Two different theoretical scenarios of inclusion of the full Coriolis force account in the problem are considered, and in both cases this leads to a reduction in the degree of inertial instability of the basic flow.