Application of the Bispectral Wavelet Analysis for Searching Three-Wave Interactions in the Spectrum of Internal Waves

G. V. Zhegulin1, ✉, A. V. Zimin1, 2

1 Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russian Federation

2 Saint-Petersburg State University, Saint-Petersburg, Russian Federation

✉ e-mail: gleb-jegulin@rambler.ru

Abstract

Purpose. The aim of the work is to test the bispectral wavelet analysis being applied as a tool for studying resonance interactions between the frequency components in the spectrum of internal waves (based on the example both of the model signals, the shape of which is similar to that of the solitons and boras, and the field observations data on temperature fluctuations resulted from the internal waves in the Gorlo Strait of the White Sea).

Methods and Results. The paper represents a technique for detecting three-wave interactions in the internal waves’ spectrum. The method is based on the bispectral wavelet analysis. It permits to identify the interharmonic correlation and the magnitude of the quadratic phase relationship arising as a result of nonlinear interactions between the signal frequency components. In the first part of the paper, efficiency of the applied method was evaluated using the example of various artificial signals with quadratic nonlinearity in order to demonstrate the method features and advantages. In its second part, the method was used to analyze the temperature profiles obtained by scanning thermohaline sounding, in which the oscillations related to passing of the internal wave groups were recorded. It is shown that the waves with the 40 min period are generated due to quadratic nonlinearity. The auto-bicoherence function values confirm the fact that the higher harmonics are formed in the 60–120 min range as a result of the three-wave interactions. They change synchronously in time, and their amplitudes are proportional, that is typical of the initial stage of the waves’ nonlinear transformation. Absence of a periodic change in the biphase sign in the considered range indicates insignificant influence of the dispersion effects upon the short-period internal waves’ structure.

Conclusions. The example of observations in the Gorlo Strait of the White Sea shows that the recorded asymmetric structure of the isotherm oscillations was formed being influenced by the three-wave interaction. Possibility of further application of the method for studying the processes of the internal waves’ nonlinear transformation and breaking is discussed.

Keywords

temperature fluctuations, internal waves, nonlinearity, auto-bicoherence, phase coupling, asymmetry, three-wave interaction

Acknowledgements

The work was carried out within the framework of the state task on theme No. 0128-2021-0014 “Wave processes, transport phenomena and biogeochemical cycles in the seas and oceans: a study of the forming mechanisms based on physical and mathematical modeling and field experimental work”. The authors are especially grateful to Justin A. Schulte (http://justinschulte.com/) for the algorithm developed on the basis of modern statistical methods for analyzing unsteady signals, and for the software packages accessed free in the network, that significantly helped in preparing the paper.

Original russian text

Original Russian Text © G. V. Zhegulin, A. V. Zimin, 2021, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 37, Iss. 2, pp. 147-161 (2021)

For citation

Zhegulin, G.V. and Zimin, A.V., 2021. Application of the Bispectral Wavelet Analysis for Searching Three-Wave Interactions in the Spectrum of Internal Waves. Physical Oceanography, 28(2), pp. 135-148. doi:10.22449/1573-160X-2021-2-135-148

DOI

10.22449/1573-160X-2021-2-135-148

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