Scattering and nonlinear transformations of internal tide beams

Abstract

The fate of internal tides as they propagate in non-uniform stratification is studied using two different numerical models, a linear and inviscid modes model (LIMM) and the nonlinear Massachusetts Institute of Technology general circulation model (MITgcm). As an internal tide beam propagates through varying density stratification, wave energy can be scattered through linear processes such as internal reflection and refraction. Scattering can lead to the splitting of beams so that the energy density of individual beams is decreased. Beam scattering can also cause horizontal ducting, or partial vertical confinement, of internal tide energy in the pycnocline and mixed layer. Two different beam scattering regimes are identified through LIMM experiments, and a non-dimensional parameter predicting the amount of internal reflection that occurs due to changing stratification is proposed. Kinetic energy from internal tide beams can also be transferred to non-tidal frequencies and vertical scales through the nonlinear generation of internal solitary waves, higher harmonics, and, depending on latitude, triadic resonant interactions. We find that interfacial waves in the pycnocline can be generated for a range of latitudes with stratification representative of the Bay of Biscay, but not with a profile representative of Hawaii. The Bay of Biscay experiments also show more horizontal ducting of energy in the pycnocline, for all frequencies. Both sets of experiments show transfers of energy to subharmonic frequencies and small vertical scales that suggest the presence of triadic resonant interactions. At latitudes where triadic resonant interactions are most active, energy transferred to subharmonic secondary waves can grow with time until it becomes greater than the energy remaining at the forcing frequency. For the Bay of Biscay experiments, degradation of the tidal beam due to triadic resonant interactions can interfere with the generation of interfacial waves in the pycnocline.