Tidal conversion into vertical normal modes by near-critical topography

The solution from linear theory for the barotropic-to-baroclinic tidal energy conversion into vertical modes is validated with numerical simulations and analytical results. The main result is the translation of the traditional critical slope condition into a mode-wise condition on the topographic height only. Our findings are then used for estimates of the global M2 tidal conversion into the first 10 vertical modes in the open ocean (excluding the continental shelves and slopes). We observe a rapid increase with mode number of the fraction of the world ocean where linear theory is invalid. In terms of conversion, which is highly variable in space, this corresponds to an even more rapid increase with mode number of the fraction of the converted energy that is strongly affected by nonlinear effects. Out of the 373.6 GW of the globally integrated conversion into modes 1-10, only 241.7 GW occur in locations where linear theory is valid. While it represents 95% for mode 1, this fraction rapidly drops with mode number to reach 27% for mode 10. Moreover, for the conversion into a single mode, we show that capping the linear solution at supercritical topography is inappropriate. Hence, linear theory appears unfit to directly quantify the role played by high-mode internal tides in the internal wave energy budget.