Superinertial internal tides propagating along the coast: dynamics and energetics revealed through topographic modes

Abstract Internal tides are an important energy source for diapycnal mixing in the ocean interior. Subinertial internal tides are known to have a cross-sectional structure that is baroclinic in deep areas but more barotropic in shallower areas, making the conventional barotropic–baroclinic decomposition ineffective to separate internal tides from surface tides. To address this issue, Tanaka introduced a “topographic mode” which represents internal motions with a barotropic vertical structure and proposed a new energy diagram enabling us to quantify the generation of subinertial internal tides. Here, the applicability of this new energy diagram to superinertial internal tides at various latitudes is investigated by idealized numerical experiments with uniform surface tides passing over a continental slope with a bump in the coastline. The calculated results show that both the topographic and baroclinic modes are generated over the bump and propagate downstream along the coast, inseparably forming a topographically modified internal Kelvin wave whose cross-sectional structure closely resembles that obtained by solving a two-dimensional eigenvalue problem for a superinertial frequency. The energy conversion rate from the surface mode to the topographic mode is about half of the energy conversion rate from the surface mode to the baroclinic mode when the tidal frequency is slightly superinertial and maintains a nonnegligible contribution even when the tidal frequency is substantially superinertial. The findings of this study indicate that the new energy diagram can be applied seamlessly across the critical latitudes and possibly provides a global distribution of the internal tide generation significantly larger than the previous estimates. Significance Statement Quantifying the generation of internal tides is essential for accurate climate modeling, since they are a major energy source of vertical mixing in the ocean. It is known that diurnal internal tides change their characteristics poleward of 30° latitude, where their motion is dominated by horizontal rotation rather than vertical oscillation. This study demonstrates that a recently proposed energy diagram for quantifying the generation of diurnal internal tides poleward of 30° latitude is also effective equatorward of 30° latitude. This is because the rotational motion remains significant even equatorward of 30° latitude, being a fundamental component of the internal tides over a sloping seafloor. The application of this energy diagram will improve the global estimate of internal tide generation.