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Modelling the interactions of near-inertial waves and vortical motion in the ocean

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Mathematics for the Fluid Earth

Co-author: Eric Danioux (University of Edinburgh)

Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) make a dominant contribution to the vertical velocity and vertical shear in the ocean; they therefore play an important role for mixing, biological productivity, pollutant dispersion and, arguably, the thermohaline circulation. An asymptotic model proposed by Young and Ben Jelloul describes the slow evolution of NIWs that results from weak dispersion and from their interactions with the quasi-two-dimensional vortical motion. We derive this YBJ model by applying a form of Whitham averaging to the variational formulation of the primitive equations for a rotating stratified fluid. This provides a direct route to the YBJ equation and elucidates its variational structure and conservation laws. We then consider the effect of turbulent vortical motion (modelled as a homogeneous random field) of a scale similar to that of the waves. Specifically, we derive a transport equation for NIWs that describes their scattering by the vortical motion and show how this scattering leads to an isotropization of the NIW field. Direct numerical simulations of the YBJ equations are used to test the predictions of the transport equation. Possible models of the two-way coupling between NIWs and vortical motion are also discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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