Study on the applicability of the high-order unidirectional internal solitary wave theoretical model
Internal solitary waves are widespread throughout the oceans, and their generation, propagation evolution, and dissipation have profound effects on the ocean environment, topography, and marine structures. Typically, two basic theoretical models are currently being developed to govern the evolution of internal solitary waves at the interface of two immiscible inviscid fluids. One is a unidirectional wave propagation model represented by the KdV (Korteweg-de Vries) equation, while the other is a
... bidirectional wave propagation model containing the MCC (Miyata-Choi-Camassa) equation. Neither of them, however, can effectively characterize the course of the evolution of large-amplitude internal solitary waves. In this paper, a modified unidirectional internal solitary wave model is established by adjusting the coefficients of the original unidirectional model. The adjusted coefficients are determined using asymptotic analysis by matching with the MCC model. The efficiency of the altered coefficients was investigated through a comparison of the modified model and the original model. The experiments on the generation of internal solitary waves with varying amplitudes have been carried out in comparison with the internal solitary wave solution of the modified equation. It's shown the modified model is suitable for describing the waveform of internal solitary waves with small, medium, and large amplitudes within the limiting amplitude of the MCC model. By quantitatively analyzing the agreement of the effective wavelength, wave speed, and waveform of steady-state internal solitary waves between the unidirectional models and the MCC model, the applicability of the modified model in characterization of the properties of steady-state internal solitary waves has been further investigated. In addition, the stability analysis of unidirectional theoretical models is performed for simulating the propagation of large-amplitude internal solitary waves under flat bottom conditions. It's found that the unidirectional models are appropriate for initiating their own internal solitary solutions provided that the numerical scheme is stable. It is shown that the modified unidirectional model can be used to characterize large- amplitude internal solitary waves, which is expected to be applied in the study of marine structure hydrodynamics.