Latitude dependence of the fate of internal tide beams

Energy from internal tide beams can be transferred to non-tidal frequencies through the generation of internal solitary waves, higher harmonics, and, depending on latitude, triadic resonant interactions. Two-dimensional MITgcm simulations forced at the boundary such as to produce an upward propagating M₂ internal tidal beam are used to examine how these nonlinear processes depend on stratification and rotation. Two stratification profiles were used: one representative of the Bay of Biscay, and one representative of Hawaii.

We find that solitary waves, indicated by the propagation of interfacial waves, can be generated where the internal tidal beam intersects the pycnocline with the Bay of Biscay stratification, but not with the Hawaii stratification profile. The Bay of Biscay experiments also show more horizontal ”ducting” of energy in the pycnocline, at both superharmonic as well as subharmonic frequencies.

Both sets of experiments show transfers of energy to subharmonic frequencies, accompanied by the appearance of energy at small vertical scales, suggesting the presence of triadic resonant interactions. Sub-M2 secondary waves are observed both equatorward and poleward of the critical latitude (29^o). Triadic resonant interaction energy transfers are largest near the critical latitude, where, away from the boundary forcing, the energy in the secondary waves can become more than three times the energy remaining at M₂. At 35^o the energy in the sub-M2 secondary waves can be up to 60% of the remaining M₂ energy. Energetic triadic resonant interactions can result in degradation of the incident tidal beam which interferes with the generation of the interfacial waves in the pycnocline.