Bispectra of Internal Tides and Parametric Subharmonic Instability

TL;DR

This paper uses bispectral analysis to identify and quantify energy transfer via parametric subharmonic instability in internal tides, demonstrating the method's effectiveness in idealized models and its challenges with real data.

Contribution

It introduces bispectral analysis as a tool to detect and measure PSI energy transfer in internal tides, linking theoretical resonance conditions with observed bispectral signals.

Findings

Bispectral transfer rates match model growth rates of daughter waves.

Bispectra identify nonlinear energy transfer terms.

Resonance conditions predict PSI wavenumber triads.

Abstract

Bispectral analysis of the nonlinear resonant interaction known as parametric subharmonic instability (PSI) for a coherence semidiurnal internal tide demonstrates the ability of the bispectrum to identify and quantify the transfer rate. Assuming that the interaction is confined to a vertical plane, energy equations transform in such a way that nonlinear terms become the third-moment spectral quantity known as the bispectrum. Bispectral transfer rates computed on PSI in an idealized, fully-nonlinear, non-hydrostatic Boussinesq model compare well to model growth rates of daughter waves. Bispectra also identify the nonlinear terms responsible for energy transfer. Using resonance conditions for an M2 tide, the locus of PSI wavenumber triads is determined as a function of parent-wave frequency and wavenumbers, latitude and range of daughter-wave frequencies. The locus is used to determine the expected bispectral signal of PSI in wavenumber space. Bispectra computed using velocity profiles from the HOME experiment are relatively noisy and the signal inconclusive.