Wave-making experiments and theoretical models for internal solitary waves in a two-layer fluid of finite depth

Abstract

A laboratory wave-making method is developed for the internal solitary wave under the condition of giving its amplitude produced by oppositely and horizontally pushing two vertical plates placed separately in the upper- and lower-layer fluids of a large-scale density stratified tank where based on the Miyata-Choi-Camassa (MCC) theoretical model, the layer-mean velocities of the upper- and lower-layer fluids induced by the internal solitary wave are used as the velocities of the two plates. On this basis, a series of experiments is conducted to explore the applicability conditions for internal solitary wave theories with stationary solutions which are Korteweg-de Vries (KdV), extended KdV (eKdV), MCC and modified KdV (mKdV) models in a two-layer fluid of finite depth respectively. It is shown that for the nonlinear parameter ε and the dispersion parameter μ defined by the total water depth, there exists a critical dispersion parameter μ0, in the case of μ μ0, the KdV model is applicable for ε ≤μ, the eKdV model is applicable for μ ε ≤√μ, as well as the MCC model is applicable for ε > √μ. However, in the case of μ ≥ μ0, the MCC model is still applicable for a wide range of ε. Furthermore, for the case where the ratio of depth between the upper- and lower-layer fluids is not close to its critical value, the mKdV model is mainly applicable for the case where the amplitude of the internal solitary wave is close to its theoretical limiting amplitude, however, the MCC model is also applicable for such a case. The investigation quantitatively characterizes the applicability conditions for four classes of internal solitary wave theories, and provides an important theoretical foundation for what kinds of theories can be chosen to model internal solitary waves in the ocean.