Assessment of KdV and EKdV theories for simulating internal solitary waves in the continental slope of the South China Sea
Lintai Rong, Xuejun Xiong, Liang Chen
Abstract
Korteweg-de Vries (KdV) and Extended KdV (EKdV) are two important nonlinear theoretical models that are most commonly used for the description of internal solitary waves (ISWs). However, most of the previous studies based on the applications of these two models focus only on laboratory-based simulations. Moreover, the modeling data in those studies were rarely compared with the in-situ measurements. In this study, three moorings were deployed to the west of Dongsha Islands of the northern South China Sea (SCS), based on the KdV and EKdV theoretical approaches, to simulate and statistically analyze 854 mode-1 ISWs and 37 mode-2 ISWs captured during the period of observation. The results from this study indicated that both theories can be used to well describe the mode-1 ISWs with η0/H<0.12 (η0 and H are the amplitude of ISW and depth of seawater, respectively). Generally, when the depth of pycnocline was not close to H/2, the EKdV theory was more accurate than the KdV theory in simulating the waveforms and vertical velocities of mode-1 ISWs. However, for mode-1 ISWs with larger amplitudes, the horizontal velocities of the upper layer calculated by the EKdV theory were extremely large. The EKdV theory was no longer applicable when the depth of pycnocline was close to H/2 and η0 exceeded its limiting value of the EKdV theory. For mode-2 ISWs, the waveforms simulated by the EKdV theory were in close agreement with the in-situ measurements. However, neither of the two theories can accurately simulate the velocities. Further, the statistical results of propagation speeds of 49 mode-1 ISWs highlighted that the EKdV theory performed slightly better than the KdV theory in calculating the propagation speed of ISWs. Finally, the MCC (Miyata-Choi-Camassa) theory was introduced as a supplement to simulate larger-amplitude ISWs. The MCC theory was found to show better performance than the above two theories in simulating the ISWs with η0/H>0.15 but the trend was opposite when η0/H<0.15.