Energy spectra analysis and bi-spectra identification of nonlinear resonant interactions of internal ocean waves

Higher order statistics (HOS) are very useful in fields where either non-Gaussianity, non-minimum phase, colored noise, or nonlinearities are important and must be accounted for. HOS have found a wide applicability in many diverse fields such as mechanical systems, biomedical signal analysis, economic time series, image and speech processing and son on. The paper illustrates bi-spectrum and its application in the oceanography area. The purpose of the present paper is twofold, namely: I) to review the bi-spectrum method and nonlinear interactions of internal waves in the ocean, especially the parametric sub-harmonic instability (PSI) for a coherence internal wave, and, II) to describe the applications of the bi-spectrum and bi-coherence to the identification of nonlinear resonant interactions of internal waves in the ocean. The bi-spectral analysis of the numerically reproduced responses of the internal wave field to the incidence of the low-mode internal wave is performed. The bi-spectrum is demonstrated to be an effective tool for identifying the nonlinear resonant interaction known as PSI in internal ocean waves.