Wave generation through the interaction of a mode-2 internal solitary wave and a broad, isolated ridge

Abstract

The passage of a mode-2 internal solitary wave (ISW) over a broad, isolated ridge was explored using both numerical simulations and laboratory experiments. At sufficient incident wave amplitude and speed, the interaction with the ridge caused a deceleration of the incident wave while also generating three wave types: a leading mode-1 ISWs, a trailing mode-1 wave-packet, and a trailing mode-2 ISW. The trailing mode-2

Hyperbolic model of internal solitary waves in a three-layer stratified fluid

“…If Ψ 2 * < 1 then straight line (16) intersects curve (15) in the square S. In this case we have two more real roots of the characteristic polynomial (Fig. 1 (d)).…”

“…The number of real roots of equation χ(λ) = 0 is determined by the number of intersections of the curve (15) with the straight line (16). Each point of interaction yields a sonic characteristic with the slope λ = w − Ψ √ a 2 ζ.…”

“…The peculiarity of this collision is that it involves trapped masses of a fluid. In recent works [15,16], the main features of the interaction of mode-2 ISWs with a narrow and broad isolated topography were investigated applying both numerical simulations and laboratory experiments. It was found that the mode-2 incident wave generates multiple internal waves and wave types from the interaction with a broad ridge at sufficiently high amplitude and wave speed.…”

Resonant coupling of mode-1 and mode-2 internal waves by topography

“…Another mechanism for the generation of mode-2 waves is local generation; that is, the release of a density front into a pycnocline which is often used in laboratory and numerical studies (Maxworthy 1980;Mehta, Sutherland & Kyba 2002;Deepwell & Stastna 2016;Carr et al 2019;Rayson et al 2019). There are several studies of the transformation of a mode-2 solitary wave over bottom topography, for example, a step (Terletska et al 2016;Liu, Grimshaw & Johnson 2019b), a narrow ridge (Deepwell et al 2017), a broad ridge (Deepwell et al 2019), a uniform slope (Carr et al 2019) and a slope-shelf (Cheng et al 2017;Yuan, Grimshaw & Johnson 2018).…”

“…2017), a broad ridge (Deepwell et al. 2019), a uniform slope (Carr et al. 2019) and a slope–shelf (Cheng et al.…”