Wave–wave interactions in a periodic chain with quadratic nonlinearity

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

Physical Oceanography ◽

10.22449/1573-160x-2021-2-135-148 ◽

2021 ◽

Vol 28 (2) ◽

Author(s):

G. V. Zhegulin ◽

A. V. Zimin ◽

◽

Keyword(s):

Wavelet Analysis ◽

Internal Waves ◽

White Sea ◽

Nonlinear Transformation ◽

Quadratic Nonlinearity ◽

The White Sea ◽

Wave Interactions ◽

Short Period ◽

Frequency Components ◽

The Waves

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.

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

Morskoy gidrofizicheskiy zhurnal ◽

10.22449/0233-7584-2021-2-147-161 ◽

2021 ◽

Vol 37 (2) ◽

Author(s):

G. V. Zhegulin ◽

A. V. Zimin ◽

◽

Keyword(s):

Wavelet Analysis ◽

Internal Waves ◽

White Sea ◽

Nonlinear Transformation ◽

Quadratic Nonlinearity ◽

The White Sea ◽

Wave Interactions ◽

Short Period ◽

Frequency Components ◽

The Waves

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 the 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.

Download Full-text