Numerical and experimental time–frequency analysis of internal waves induced by a submerged body

Abstract

Time–frequency analysis is widely applied in Kelvin ship waves. However, limited studies have been conducted on the time–frequency features of internal waves. In this study, spectrograms used to visualize the frequencies of the internal waves generated by a submerged body are studied using a short-time Fourier transform. A linear dispersion curve and numerical model are introduced considering an idealized situation. The linear dispersion curve indicates wave frequency variation with time. The effects of parameters on the dispersion curve are discussed for a linear density profile and three-layer density profile. The dispersion curve presents upper and lower branches corresponding to the divergent and transverse wave components, respectively. In contrast to surface waves, the upper-branch curve for internal waves continues to increase and finally levels to the middle Brunt–Vaisala (BV) frequency Nm of the density profile, whereas the lower branch curve continues to decrease and finally approaches a constant value. The numerical simulation provides idealized spectrograms of the linear internal waves. The linear dispersion curve provides an excellent prediction of the dominant wave signals. The high-intensity portion in the spectrograms is confined to the lower branch for a low Froude number, whereas for a larger Froude number, the high-intensity portion follows the upper branch but decays rapidly over time. The spectrograms obtained by the model test reveal that the high-color-intensity portion can be categorized into leading, reflected, nonlinear, and low-frequency regions. The experimental results also reveal that the model travel length is a critical factor affecting internal waves.