Two-dimensional resonant triad interactions in a two-layer system

Choi, Woo-Young; Chabane, Malik; Taklo, Tore Magnus Arnesen

doi:10.1017/jfm.2020.824

Cited by 10 publications

(10 citation statements)

References 35 publications

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“…In figure 2(a), we present contours of the critical rescaled depth, ζ c , in the (ξ 1 , ξ 2 )-plane, restricted to the region demarcated by equation (11). Consistent with the limits lim ζ→0…”

Section: Determining the Critical Depthsupporting

confidence: 59%

“…In this setting, the density difference across the fluid-fluid interface has a strong influence of the system dynamics; it seems plausible, therefore, that additional resonances may be excited in this configuration, relative to the liquid-air interface considered herein. Notably, the anticipated resonances would arise across a single interface, in contrast to the cross-interface resonances explored in previous investigations [1,54,25,53,56,11]. Finally, exploring the influence of parametric forcing [31] on resonant triads arising for two-layer flows opens up exciting new vistas in nonlinear resonance induced by confinement.…”

Section: Discussionmentioning

confidence: 87%

“…Indeed, exploration of the nonlinear dynamics may reveal additional resonant triads arising beyond the small-wave-amplitude limit explored herein. Of similar interest is the fluid evolution when multiple triads are excited at a single depth, with the potential for energy exchange via triad-triad interactions [35,15,13,11]. The simulation of free-surface gravity waves in non-circular cylinders presents a more formidable challenge, however, except for cylinder cross-sections that possess a tractable eigenmode decomposition.…”

Section: Discussionmentioning

confidence: 99%

“…an expression valid when 0 < ζ c 1 and ξ 1 + ξ 2 < 1 (see equation (11)). Alternatively, one may deduce from equation ( 15) that the contours of ζ c satisfy the approximate form…”

Section: Determining the Critical Depthmentioning

confidence: 99%

“…To demonstrate the potential for the simultaneous excitation of two triads within a circular cylinder of finite depth, we consider two scenarios: (i) the excitation of two triads that share a common wave mode; and (ii) the excitation of two triads that do not share any common wave modes. Heuristically, case (ii) is more common than case (i) owing to the number of similar fluid depths in table 1; however, case (i) will likely generate a far richer set of dynamics owing to the nonlinear interaction between the two triads [35,15,13,11]. As an example of case (i), we consider triads 21 and 24 in table 1, with nearby critical depths h c,1 = 0.21395 and h c,2 = 0.23678, respectively.…”

Section: Circular Cylindermentioning

confidence: 99%

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Resonant triad interactions of gravity waves in cylindrical basins

Durey¹,

Milewski²

2023

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We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are impossible for gravity waves in laterally unbounded domains; we demonstrate, however, that horizontal confinement of the fluid may induce resonant triads for particular fluid depths. For any three correlated wave modes arising in a cylinder of arbitrary cross-section, we prove necessary and sufficient conditions for the existence of a depth at which nonlinear resonance may arise, and show that the resultant critical depth is unique. We enumerate the low-frequency triads for circular cylinders, including a new class of resonances between standing and counter-propagating waves, and also briefly discuss annular and rectangular cylinders. Upon deriving the triad amplitude equations for a finite-depth cylinder of arbitrary cross-section, we deduce that the triad evolution is always periodic, and determine parameters controlling the efficiency of energy exchange. In order to excite a particular triad, we explore the influence of external forcing; in this case, the triad evolution may be periodic, quasi-periodic, or chaotic. Finally, our results have potential implications on resonant water waves in man-made and natural basins, such as industrial-scale fluid tanks, harbours and bays.

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Section: Determining the Critical Depthsupporting

confidence: 59%

Section: Discussionmentioning

confidence: 87%

Section: Discussionmentioning

confidence: 99%

“…an expression valid when 0 < ζ c 1 and ξ 1 + ξ 2 < 1 (see equation (11)). Alternatively, one may deduce from equation ( 15) that the contours of ζ c satisfy the approximate form…”

Section: Determining the Critical Depthmentioning

confidence: 99%