Transformation of mode-2 internal solitary wave over a pseudo slope-shelf

Abstract

Numerical simulations are performed to investigate the effect of wave amplitude in a numerical wave tank on the evolution of a convex mode-2 internal solitary wave (ISW) propagating over a pseudo slope-shelf. A finite volume method based on a Cartesian grid system is adopted to solve the Navier-Stokes equations using Improved Delayed Detached Eddy Simulation model for the turbulent closure. Numerical results reveal three types of waveform during wave generation on the flat bottom: (1) pseudo vortex shedding in the case of very large initial amplitude; (2) PacMan phenomenon in large amplitude; and (3) smooth mode-2 ISW for small amplitude. During wave propagation on the plateau, the first type of waveform induces a quasi-elevated mode-1 ISW; the second generates chaotic internal waves with significant reduction in amplitude; while the third renders a slightly deformed mode-2 ISW across the plateau. Moreover, the decrease in the magnitude of leading trough is more intense than that in the leading crest due to strong wave-obstacle interaction in the case of very large initial wave amplitude.

Shoaling mode-2 internal solitary-like waves

“…This finding adds particular relevance to comparisons of the shoaling behaviours observed by Cheng et al (2017) for the slope-shelf topography with those reported herein for constant slope cases (without a shelf). Cheng et al (2017) considered the same undisturbed, stable density configuration as the present paper, namely two homogeneous layers of different density but equal thickness, separated by a thin pycnocline. The mid-level of the undisturbed pycnocline was prescribed to be always above the plateau section of the slope-shelf topography and a single slope with a fixed length and angle θ (θ = 6 • ; s = tan θ = 0.105) was considered.…”

“…Test runs conducted by Cheng et al (2017) to replicate the laboratory study by Carr et al (2015) for constant depth conditions showed excellent agreement between numerical simulations and laboratory data. This finding adds particular relevance to comparisons of the shoaling behaviours observed by Cheng et al (2017) for the slope-shelf topography with those reported herein for constant slope cases (without a shelf). Cheng et al (2017) considered the same undisturbed, stable density configuration as the present paper, namely two homogeneous layers of different density but equal thickness, separated by a thin pycnocline.…”

“…There is already a substantial literature on the modelling of mode-2 waves for cases of constant depth and many of these studies (Davis & Acrivos 1967;Maxworthy 1980;Kao & Pao 1980;Stamp & Jacka 1995;Terez & Knio 1998;Schmidt 1998;Stastna & Peltier 2005;Gavrilov & Lyapidevski 2009;Salloum et al 2012;Olsthoorn et al 2013;Brandt & Shipley 2014;Carr et al 2015;Deepwell & Stastna 2016;Cheng et al 2018) have contributed significantly to our understanding of the generation mechanisms of mode-2 waves, their structural, stability and kinematic properties and their ability to transport mass. Much recent interest has focussed on the effects of bottom topography upon the above properties, with laboratory and computational studies being undertaken by Gavrilov & Lyapidevski (2011); Guo & Chen (2012); Yuan et al (2018); Cheng et al (2017) for slope-shelf topography and Deepwell et al (2017) for the case of a train of mode-2 ISWs encountering a narrow, two-dimensional, Gaussian-profile ridge. The combined numerical and laboratory investigation undertaken in the Deepwell et al (2017) study provided, for the first time, clear indications of flow separation and vortex formation on the upward boundary slope of the topography as a characteristic property of shoaling mode-2 waves of large and moderate amplitude.…”

“…The combined numerical and laboratory investigation undertaken in the Deepwell et al (2017) study provided, for the first time, clear indications of flow separation and vortex formation on the upward boundary slope of the topography as a characteristic property of shoaling mode-2 waves of large and moderate amplitude. The numerical modelling study by Cheng et al (2017) considered the distortion caused to mode-2 waves by passage over a combined slope-shelf topography placed in a channel having the same dimensions and gate release wave generation mechanism in the experiments described by Carr et al (2015); Deepwell et al (2017) and the present investigation. Test runs conducted by Cheng et al (2017) to replicate the laboratory study by Carr et al (2015) for constant depth conditions showed excellent agreement between numerical simulations and laboratory data.…”

“…The numerical modelling study by Cheng et al (2017) considered the distortion caused to mode-2 waves by passage over a combined slope-shelf topography placed in a channel having the same dimensions and gate release wave generation mechanism in the experiments described by Carr et al (2015); Deepwell et al (2017) and the present investigation. Test runs conducted by Cheng et al (2017) to replicate the laboratory study by Carr et al (2015) for constant depth conditions showed excellent agreement between numerical simulations and laboratory data. This finding adds particular relevance to comparisons of the shoaling behaviours observed by Cheng et al (2017) for the slope-shelf topography with those reported herein for constant slope cases (without a shelf).…”