Eulerian flows induced by internal tides

Tidal flow over bottom topography in the ocean generates beams in the near field that evolve to become dominantly horizontally propagating vertical mode-1 internal tides. Previous work has shown that two-dimensional (spanwise-infinite) tides self-interact to excite mode-1 superharmonics with double the horizontal wavenumber, and that successive near-resonant interactions between the parent tide and superharmonics can lead to a cascade which results in the formation of a solitary wave train, in good agreement with the predictions of the KdV and Ostrovsky equations. In this work we focus on the self-interaction of the parent tide and superharmonics that induce an Eulerian mean flow. Whether or not superharmonics grow to substantial amplitude, the forcing of the induced Eulerian mean flow is constant. However, the forcing is not resonant resulting in structures which are a superposition of horizontally long, vertical modes. On the f-plane, the structure is the same as the Stokes drift, but oscillates at frequency f at amplitudes between zero and minus twice the Stokes drift amplitude. If f=0, only horizontally modulated internal tides induce a mean flow that gradually grows to be larger than the magnitude of the Stokes drift.