We study the generation and propagation of internal tides (internal gravity waves at tidal frequency) in a rotational and inhomogeneous ocean background with spatially varying mean flow, buoyancy and topography. For interaction in a vertically bounded domain, the field of internal tide (IT) can be expanded using a set of modal basis functions which capture its vertical profile, with the modal amplitudes varying in the horizontal space and time.

We started by deriving the evolution equations of the modal amplitudes, including terms describing the interactions with the mean field. This provides a reduced-order model of the IT since most of its energy is contained in the low-mode waves. These equations are verified using direct simulations of the primitive equations for two regional flows around the Middle Atlantic Bight and the Palau Island (see figure 1 for an illustration of the former). Significant interactions of the IT with the mean field are physically present at the continental and insular shelf break, and the gulf stream. The modal energy budget of the IT at these regions is quantified by considering the effects of mean-flow advection, energy exchange with the mean field and topographic modal conversion.

We also considered the interaction of IT with a large-scale barotropic current for which the evolution of each vertical mode can be decoupled. Under this circumstance the derived modal evolution equation is reduced to the conservation of modal wave action, and a WKB approach is established to analyze the interaction. We derived the analytical solutions of the modulation of wavenumber and energy of a modal IT propagating into a collinear current (see figure 2 for a schematic plot). These solutions have profound implications on the propagation and dissipation of IT in the ocean.

Publication:

Pan, Y., Haley, P.J. and Lermusiaux, P.F.J. 2020, Interaction of internal tide with an inhomogeneous and rotational ocean background, Journal of Fluid Mechanics, sub-judice.