Internal solitary wave (ISW) is a kind of nonlinear internal waves commonly seen in the shallow water, which has the characteristics of large amplitude, short period and strong current velocity. With the distribution of the temperature and salinity in the water column perturbed by ISWs, the sound speed profile becomes range-dependent, thus affecting the underwater acoustic propagation characteristics. ISWs usually propagate at a speed of O(1) m/s, and moving internal waves cause the energy in each acoustic mode to fluctuate dramatically. In this paper, the modal intensity is defined as the square of the modular value of the modal coefficient, and is used to measure the sound energy contained in each mode. Based on the coupled mode theory, this paper derives the expression of the acoustic modal intensity during the propagation of internal waves, and the modal intensity is represented as the linear superposition of the oscillation term and the trend term. Most of previous works are limited to studying time-varying characteristics of the acoustic modal intensity during the propagation of internal waves in the time domain or frequency domain separately. In this paper, the mechanism of modal intensity fluctuations is studied simultaneously in the time domain and in the frequency domain with the aid of the short-time Fourier transform. The theoretical derivation and numerical simulation both show that the internal solitary wave causes the energy exchange among acoustic modes, that is, the mode coupling. The dynamic propagation of internal waves further causes the modal interference, which is manifested as an oscillating term in the modal intensity, and causes the modal intensity to fluctuate rapidly with time. The amplitude of the trend term changes over time due to the mode stripping effect (the difference in attenuation coefficients between different modes), which in turn adds a time-varying offset to the oscillations caused by the modal interference. The overall trend of the modal intensity and the time-varying characteristics of the amplitude of each frequency component in the oscillation term are closely associated with the modal attenuation. Meanwhile, the depth-integrated intensity is chosen as the measure of the total received acoustic intensity, and the influence of modal intensity fluctuations on the acoustic energy at the receivers during the propagation of internal waves is studied. It is demonstrated that the modal intensity with high energy which oscillates most dramatically will dominate the temporal variation of the received acoustic energy.
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