Experimental investigation of the second-mode internal solitary wave in continuous pycnocline and the applicability of weakly nonlinear theoretical models

Abstract

The research on the propagation and evolution of the second-mode internal solitary waves(ISWs) is receiving more and more attention. In this study, second-mode internal solitary waves in continuous stratification are physically simulated in a laboratory-stratified fluid flume. Meanwhile, the second-mode ISWs and their induced flow field in the same stratification environment are solved based on the eigenvalue problem of the TG equation (Taylor-Goldstein), combined with the weakly non-linear ISW theoretical models. The experimental and theoretical results show that the symmetry of the second-mode ISW wave-flow field can be improved as the thickness ratio of the upper fluid layer and lower one approaches 1. The ISW speed and horizontal and vertical velocity range values in the continuous pycnocline are positively correlated with the changing ISW amplitude, while only the wavelength is negatively correlated with the iSW amplitude. The waveflow fields of the second-mode ISWs calculated by Korteweg-de Vries (KdV) and extended KdV (eKdV) models in the large amplitude cases are more consistent with the experimental results than those in the small amplitude cases. The two theoretical models used to describe second-mode ISWs can be significantly improved when the thickness ratio of the upper and lower fluid layers approaches 1. In this case, the eKdV model is more applicable than the KdV model.