The Evolution of Superharmonics Excited by Internal Tides in Non-Uniform Stratification

The mechanism by which energy cascades from the large scale low-mode internal tides to smaller scales where mixing and dissipation can act remains an open question. In this work, the excitation of near-resonant superharmonics are investigated for their possible role in extracting energy from the mode-1 (“parent”) internal tide. A time dependent theory for the evolution of superharmonics generated by the nonlinear self-interaction of a mode-1 internal tide in non-uniform stratification is developed and compared to numerical simulations. With analogy to a forced harmonic oscillator, for a system with realistic ocean stratification the excited superharmonics are found to be close to resonance, this being enhanced at low latitudes. Weakly nonlinear theory is developed that takes into account the energy transfer between the original `parent' mode and the generated superharmonic. The new coupled system is shown to possess a conservation law evocative of energy conservation, and well-predicts the beating frequency and amplitude of the superharmonic interacting with the parent. A primitive analysis with realistic oceanic parameters shows that superharmonics of internal tides could be an important mechanism by which energy is lost from the mode-1 internal tide, and it is suggested that near the equator this mechanism could be so strong as to lead to further cascade to smaller scales.