Study on applicability of internal solitary wave theories by theoretical and numerical method

It is essential to distinguish the applicable range of theories of internal solitary waves (ISWs). Numerous numerical simulations and theoretical calculations with wide ranging thickness ratios beta = h1/h2 (0.11 < beta < 0.43) and amplitude parameters alpha = a/h1 (0.05 < alpha < 2.11), where h1 and h2 are the thicknesses of upper and lower layer, respectively, a is the amplitude of ISW, have been conducted to compare the characteristics among the theoretical and numerical results. Six common theories of ISW, including KdV, eKdV, mKdV, MCC, KB, and KAS, are compared to optimize the theory for different thickness ratios and amplitude conditions. Through extensive theoretical calculations, a diagram of the applicable range of theories was proposed based on the ratio between the amplitude parameter alpha to thickness ratio beta and the square of the long wave parameter e2 = H2/lambda 2. The diagram was validated by comparing the numerical and theoretical results. Based on the numerical data, the optimal applicable ranges of the KdV theory (0.05 < alpha < 0.22) and eKdV and MCC (0.22 < alpha < 2.11) in finite depth and specified layer thickness ratio configurations are given. For application of ISW theories, the diagram of applicable range is recommended for selecting a better theory.