The model of the uniform slab model of the mixed layer which was previously analyzed for stability (Kroll, 1982) is modified to include inertial oscillations in the mean flow. The results reflect the nature of the parallel flow instability produced by the steady component of the mean flow combined with the nature of a parametric instability produced by the oscillating component of the mean flow. This model is much more likely to produce unstable perturbations with a near-inertial frequency than the steady mean model which reinforces the contention that the instability can be a source of vertically propagating inertial oscillations. Also certain frequencies that are integral multiples of the inertial frequency above a near-inertial frequency can be significant in the perturbation. The energy flux associated with these frequencies predominates as the inertial oscillations in the mean flow become significant. This could produce a significant energy flux from the mean flow.
Kroll, John. 1984. "An unstable uniform slab model of the mixed layer as a source of downward propagating near-inertial motion Part 2: Unsteady mean flow." Journal of Marine Research 42, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1709