Lagrangian transport by internal tides and their superharmonic cascade

Modulated internal tides induce both a Stokes drift and an Eulerian induced flow, the sum of which gives the Lagrangian transport of passive tracers, such as non-inertial microplastics. In realistic ocean stratification, the Eulerian flow dominates over the Stokes drift and, at the surface, it flows retrograde to the direction of propagation of the waves. This suggests that floating plastics are carried toward the source of the internal tide. On the other hand, the internal tide also excites superharmonics with double the horizontal wavenumber of the internal tide and nearly double the frequency. Particularly in the tropics where the Coriolis parameter is small, the superharmonics are nearly resonant with the internal tide, growing to large amplitude and themselves exciting superharmonics. This cascade leads to the formation of solitary waves, which have an associated surface Lagrangian transport in the direction of the waves. This work will present theory and numerical simulations illustrating the competition between the retrograde surface Eulerian transport of the parent internal tide and the prograde surface Lagrangian transport of the solitary waves it generates.