Coupled triads in the dynamics of internal waves: Case study using a linearly stratified fluid

Pan, Q.; Peng, N. N.; Chan, Hiu Ning; Chow, K. W.

doi:10.1103/physrevfluids.6.024802

Cited by 7 publications

(6 citation statements)

References 55 publications

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“…We focused on the case where the common member is a daughter wave (passive mode). This is in sharp contrast with our previous work [7], where the common member was the parent wave (active mode). Moreover, rogue modes, instead of plane waves, were used as initial conditions.…”

Section: Discussioncontrasting

confidence: 99%

“…The magnitude of the interaction coefficients may change substantially with depth H, but the variations tend to level off for the limits of small and large values of H, as illustrated in Figure 2. Compared with the situation of coupled triads with the common member being a parent wave (or active mode) in the literature, the signs of the interaction coefficients are similar [7]. More precisely, two daughter waves (or passive modes) are always of the same sign in one isolated triad, while the sign of the parent wave (or active mode) is opposite.…”

Section: Formulation Of the Triad Resonancementioning

confidence: 81%

“…Moreover, rogue modes, instead of plane waves, were used as initial conditions. While our earlier work included time dependence only [7], spatial dependence is incorporated here. Generally the signs of the interaction coefficients are critical for the energy transfer process.…”

Section: Discussionmentioning

confidence: 99%

“…Triad resonances consisting entirely of internal waves of stratified fluids have been investigated from different perspectives in the literature. The stabilities of one isolated triad and two coupled triads were analyzed in a uniformly stratified shear flow [6,7]. In physical oceanography, triad resonance has also been suggested as a possible mechanism for internal wave dissipation [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…The evolution equations can be derived, and the dependence of the interaction coefficients on the precise fluid properties can be demonstrated explicitly. Furthermore, coupling can enhance the growth rates of the instabilities compared to those exhibited by an isolated triad [7].…”

Section: Introductionmentioning

confidence: 99%

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Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Pan¹,

Yin²,

Chow³

2021

JMSE

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Internal waves in a stratified fluid with a constant buoyancy frequency were studied, with special attention given to rogue modes, extreme waves, dynamical evolution, and Fermi–Pasta–Ulam–Tsingou type recurrence phenomena. Rogue waves for triads in a general physical setting have recently been derived analytically, but the implications in a fluid mechanics context have not yet been fully assessed. Numerical simulations were conducted for cases of coupled triads where the common member is a daughter wave mode. In sharp contrast with previous studies, rogue modes instead of plane waves were used as the initial condition. Furthermore, spatial dependence was incorporated. Rogue or extreme waves in one set of triads provided a possible mechanism for significant energy transfer among modes of the internal wave spectrum, in addition to the other known theories, e.g., weak turbulence. Remarkably, Fermi–Pasta–Ulam–Tsingou recurrence types of growth and decay cycles arose, similarly to those observed for surface gravity wave groups governed by the cubic nonlinear Schrödinger equation. These mechanisms will enhance our understanding of transport processes in oceans.

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Section: Discussioncontrasting

confidence: 99%

Section: Formulation Of the Triad Resonancementioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Pan¹,

Yin²,

Chow³

2021

JMSE

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The 3-wave resonant interaction model: spectra and instabilities of plane waves

Romano,

Lombardo,

Sommacal

2023

Z. Angew. Math. Phys.

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The three wave resonant interaction model (3WRI) is a non-dispersive system with quadratic coupling between the components that finds application in many areas, including nonlinear optics, fluids and plasma physics. Using its integrability, and in particular its Lax Pair representation, we carry out the linear stability analysis of the plane wave solutions interacting under resonant conditions when they are perturbed via localised perturbations. A topological classification of the so-called stability spectra is provided with respect to the physical parameters appearing both in the system itself and in its plane wave solution. Alongside the stability spectra, we compute the corresponding gain function, from which we deduce that this system is linearly unstable for any generic choice of the physical parameters. In addition to stability spectra of the same kind observed in the system of two coupled nonlinear Schrödinger equations, whose non-vanishing gain functions detect the occurrence of the modulational instability, the stability spectra of the 3WRI system possess new topological components, whose associated gain functions are different from those characterising the modulational instability. By drawing on a recent link between modulational instability and the occurrence of rogue waves, we speculate that linear instability of baseband-type can be a necessary condition for the onset of rogue wave types in the 3WRI system, thus providing a tool to predict the subsequent nonlinear evolution of the perturbation.

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Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg–de Vries equation in a fluid

et al. 2021

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Fluids are studied in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a (3+1)-dimensional Korteweg-de Vries equation in a fluid. Bilinear form and N -soliton solutions are obtained, where N is a positive integer. Via the N -soliton solutions, we derive the higher-order breather solutions. We observe that the interaction between two perpendicular first-order breathers on the x − y and x − z planes and the periodic line wave interacts with the first-order breather on the y − z plane, where x, y and z are the independent variables in the equation. Furthermore, we discuss the effects of α, β, γ and δ on the amplitudes of the second-order breathers, where α, β, γ and δ are the constant coefficients in the equation: Amplitude of the second-order breather decreases as α increases; Amplitude of the second-order breather increases as β increases; Amplitude of the second-order breather keeps invariant as γ and δ increase. Via the N -soliton solutions, hybrid solutions comprising the breathers and solitons are derived. Based on the Riemann theta function, we obtain the periodic-wave solutions. Furthermore, we find that the periodic-wave solutions approach to the one-soliton solutions under certain limiting condition.

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Coupled triads in the dynamics of internal waves: Case study using a linearly stratified fluid

Cited by 7 publications

References 55 publications

Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

The 3-wave resonant interaction model: spectra and instabilities of plane waves

Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg–de Vries equation in a fluid

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