The evolution of superharmonics excited by internal tides in non-uniform stratification (Journal of Fluid Mechanics, 2021)

Abstract

A weakly nonlinear 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. The forcing by the internal tide is found to excite near-pure mode-1 superharmonics whose natural frequency is moderately different from twice the internal tide frequency. Consequently, the superharmonics undergo a slow periodic growth and decay that is comparable to an acoustic ‘beat’. At low latitudes the beat frequency is smaller and the superharmonics can grow to larger amplitude, allowing for the possibility of a superharmonic cascade.