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Interactions of Internal Tides with a Heterogeneous and Rotational Ocean

Pan, Y., P.J. Haley, Jr., and P.F.J. Lermusiaux, 2020. Interactions of Internal Tides with a Heterogeneous and Rotational Ocean. Journal of Fluid Mechanics, sub-judice.

We consider the interactions of internal tides (ITs) with a dynamic, rotational, and heterogeneous ocean, and spatially varying topography. The IT fields are expanded using vertical modal basis functions, whose amplitudes vary horizontally and temporally. We obtain the evolution equations of modal amplitudes and energy including simultaneous three-way interactions with the mean flow, buoyancy, and topography. We apply these equations to an idealized and two realistic data-assimilative primitive equation simulations. We find that significant interactions of ITs with the background fields occur at topographic features and at significant currents when the scales of the background and ITs are similar. In local hot-spots, the new three-way interaction terms when compared to the total modal conversion are found reach up to 10-30% at steeper topography and about 50% in the Gulf Stream. For the interactions of ITs with a large-scale barotropic current, our modal energy equation reduces to the conservation of modal wave action. Using a WKB approach, we derive analytical solutions of the modulation of wavenumber and energy of an IT propagating into a collinear current. For a following current, the wavelength is stretched and amplitude is reduced, with the degree of modulation determined by |f0|, the ratio of inertial to tidal frequencies. For an opposing current, a critical value of |f0| exists, below and above which the waves show remarkably different behaviors. The critical opposing current speed which triggers the wave focusing/blocking phenomenon is obtained and its implication on the propagation and dissipation of ITs is discussed.