Assessment of KdV and EKdV theories for simulating internal solitary waves in the continental slope of the South China Sea. (1st March 2023)

• Record Type: Journal Article
• Authors: Rong, Lintai; Xiong, Xuejun; Chen, Liang
• Is Part Of: Continental shelf research. Volume 256(2023)
• Publication Date: 2023-03-01
• Subjects: Internal solitary waves (ISWs) -- Korteweg-de Vries (KdV) -- Extended Korteweg-de Vries (EKdV) -- Mooring observations -- South China Sea (SCS); Continental shelf -- Periodicals; Submarine geology -- Periodicals; 551.41
• DOI: 10.1016/j.csr.2023.104944
• Languages: English
• ISSNs: 0278-4343

Abstract

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 η 0 / H < 0.12 ( η 0 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 The EKdV theory was no longer applicable when the depth of pycnocline was close to H / 2 and η 0 exceeded its limiting value of the EKdV theory.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 η 0 / H > 0.15 but the trend was opposite when η 0 / H < 0.15 . Highlights: Three nonlinear theories of ISWs were evaluated systematically based on the in-situ data. The applicable scope of three nonlinear theories was given in this study. A new method for calculating the propagation speed and direction of the ISWs is proposed.