Interactions between inertial oscillations and geostrophic flows in the upper ocean

Near-inertial waves are generated in the ocean’s mixed layer by strong winds with large horizontal scales, representing nearly half of the energy transferred to the ocean by atmospheric forcing. These oscillations are superimposed on the balanced mesoscale eddy field, which acts to focus and refract the waves, speeding up their propagation into the abyss. The detailed nature of the interaction between near-inertial waves and eddies has been studied by a number of researchers, but in different parameter regimes, which can be characterized by the relative strength of the waves' dispersion: strong, weak, or very weak (depending on the relative magnitude of the Rossby number of the balanced flow and the Burger number of the baroclinic inertial waves). In the present work we formulate a unified treatment of the different regimes, and demonstrate, theoretically and numerically, their relative importance in the natural evolution of a near-inertial wave.

To illuminate the processes, we first explore the dynamics of the regimes, and demonstrate inter-regime transitions, in a one-dimensional rotating shallow water model with an imposed geostrophic flow. We follow this with a more detailed investigation, especially for the strong dispersion limit, in the hydrostatic Boussinesq equations. Our results include detailed descriptions of the waves' dynamics over three different interaction time scales and feature the formation of small-scale inertial waves trapped in the upper ocean, as well as waves that propagate vertically into the deep ocean within a few inertial periods. On even longer timescales, of the order inverse squared Rossby number, the kinetic energy of the geostrophic flow is seen to modulate these modes leading to additional vertical dispersion.

Time permitting, we will also discuss recent demonstrations of an energetic interaction between balanced flow and near inertial waves that occurs in a distinct parameter regime, applicable when the wave energy is large compared to the eddy energy. Using multiscale asymptotic analysis in the fully nonlinear shallow water equations, we derive a coupled model that captures the joint slow evolution of inertial waves and geostrophic balanced flow. The interaction is also examined by numerical simulation of an initial value problem in the shallow water equations.