Coupling between oceanic near-inertial waves and balanced flow

William Young
University of California, San Diego (UCSD)

I’ll derive and discuss a set of coupled equations describing the co-evolution of balanced mean flow with the near-inertial part of the oceanic internal wave field. The balanced component of flow evolves according to a generalization of the familiar quasigeostrophic equation; there is extra contribution to the potential vorticity which is quadratic in the amplitude of the near-inertial wave field. The near-inertial part of the solution is described concisely by a complex field --- the "back-rotated velocity” — which evolves via a Schroedinger-like equation. This model system is obtained by application of straightforward two-time scale perturbation theory to the Boussinesq equations. This derivation is an alternative to the generalized lagrangian mean approach, currently pursued by other investigators. Neither route provides a totally consistent reductive derivation of the coupled system. But the importance of understanding the interaction of the near-inertial spectral peak with slowly evolving ocean currents justifies slight epsilonic dishonesty.

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