Tidal currents flowing over rough bathymetry generate internal tides. These internal waves with tidal frequency can be decomposed into vertical modes. Low modes generally travel thousands of kilometers, until they break due to shear flow instabilities, while high modes are believed to break close to the generation site. The power released by breaking internal tides is thought not only to shape the overturning circulation, but also to mix the upper ocean. Both processes have a large influence on the climate system, most notably for their key role in regulating the heat and carbon uptake by the ocean.

The generation of internal tides, or tidal conversion, can be calculated from the bottom topography, the ocean stratification and the tidal currents. Global computations of the tidal conversion have been based on linear wave theory. However, such linear calculations are only valid if the seafloor slope is subcritical, and it is not known how to treat supercritical slopes. This is especially true for the conversion decomposed into vertical modes, which, taken individually, behaves very differently from the total conversion (the sum of the contributions from all modes).

In the first paper of this thesis, we looked into the validity of linear theory in the supercritical limit. Specifically, we translated the critical slope condition, a notion defined for the superposition of all modes, into a mode-wise condition on the topographic height. The findings were applied to estimates of the global M₂-tide conversion into the first 10 vertical modes (in the open ocean, excluding the continental shelves and slopes). The results unveil the rapid increase with mode number of the oceanic area where linear theory fails. In terms of conversion, this shows that linear theory is unadapted to quantify the role played by high modes in closing the internal wave energy budget.

Typically, continental slopes are supercritical, and hence locations where the linear theory fails. Because of their characteristic shape, they are also an important source of low-mode internal tides. In the second paper of this thesis, we constructed a computationally inexpensive method to compute the tidal conversion by continental slopes and applied it at the global scale. It uses the usual observational data as inputs but relies on a reduced-physics numerical model rather than on linear theory to estimate the tidal conversion.

Unveiling the global pattern of the dissipation of internal tides (i.e. where they break) has been a challenging objective for a few decades. This can be explained by the lack of suitable observations to compare theory with. Until recently, the only observational data of internal tides with global coverage were based on satellite altimetry. However, only the part of the wave field that is exactly phase-locked to the astronomical forcing can be identified from altimetry data.

In the third paper of this thesis we created a new observational data set of internal tides, with global coverage, based on Argo park-phase data. These data are recorded while the floats are adrift at 1000 m depth, between two vertical profiling sequences. Thanks to the high sampling rate of Argo floats, the records capture the full amplitude of the waves, including the non-phase-locked part. This component turned out to be several times larger than previously thought. In the fourth paper of this thesis, we validated the internal tides in a realistic global ocean simulation with Argo data. Incidentally, this also worked to validate the Argo observations.