Internal solitary wave has been observed with different modes in the oceans, and mode-2 ISW is significant. In order to study the spatiotemporal variations while a mode-2 ISW in different amplitudes propagating over a pseudo slope-shelf, a finite volume is employed to solve the Navier-Stokes equations using IDDES model for the turbulent closure. Numerical results exhibit the PacMan phenomenon when a steady and symmetric waveform of a mode-2 ISW propagates in deep water. Moreover, a series of mode-2 ISWs generates on a flat bottom with amplitude decreasing during wave transmission. As waves encounter with the front slope of a submerged obstacle, the interaction induces unstable flow field and leads to the separation of wave crest from its leading wave. For the evolution of wave amplitude, the decrease of the leading trough is more obvious than that of the leading crest. However, the vorticity dissipation of the former is less than that of the latter. Not like a mode-1 ISW occurring hydraulic jump on the front slope, a mode-2 ISW separates on the front face of a slope-shelf.


In the ocean with density stratified fluid, internal solitary waves (ISWs) are usually generated by tide-current-topography interaction. The amplitude of a mode-1 ISW in the South China Sea (SCS) usually reaches 170 m with strong velocity difference exceeding 2.4 ms−1 between its upper and lower water layers (Chang et al., 2008), therefore, an ISW could have significant ramification not only in marine ecology but also on engineering works in the ocean (Bourgault et al., 2014; Lamb, 2014). Based on the field observations (Yang et al, 2004; Dickinson et al., 2012), the gradient of the continental shelf around Dong-Sha island is mildly sloped (~ 0.07), but that in the deeper water (150 ~ 200 m) from the shelf is rather steep (> 0.6). Abundant literature is available on the physical mechanisms that generate the mode-1 ISW and the wave transformation, arising from field observations (Alford et al., 2015; Lamb, 2014), laboratory experiments (Cheng and Hsu, 2014; Sutherland et al., 2015) and numerical simulations (Grimshaw et al., 2014; Lamb and Warn-Varnas, 2015). During the several years, mode- 2 ISWs trailed after a model-1 ISW were also found in the ocean (Ramp et al., 2015; Shroyer et al., 2010; Yang et al., 2009). Moreover, two types of mode-2 ISW, including convex and concave, are available in the real fluid (Carr et al., 2015; Deepwell and Stastna, 2016). The concave ones exist in a thick pycnocline without a trapped core; consequently, they are seldom investigated in a stratified ocean. Hence, the type of convex is almost discussed in the studies.

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