Solitary interfacial hydroelastic waves

Părău, Emilian

doi:10.1098/rsta.2017.0099

Cited by 9 publications

(5 citation statements)

References 27 publications

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“…Similar analyses have been performed on related geometries, including waves on internal flow interfaces under an elastic sheet by Wang et al (2014), finite-depth shear flow under an elastic sheet by Wang, Guan & Vanden-Broeck (2020), flow in a fluid separated by an internal elastic sheet by Părău (2018), and flow contained between two elastic sheets by Blyth, Părău & Vanden-Broeck (2011). When studying nonlinear geometries, care must be taken in choosing an appropriate model for the elastic sheet; Milewski & Wang (2013) investigated the effect of different elastic sheet models on nonlinear surface waves, and demonstrated that the choice of elastic sheet model can have a significant impact on the observed behaviour in nonlinear problems.…”

Section: Introductionmentioning

confidence: 74%

Exponential asymptotics for elastic and elastic-gravity waves on flow past submerged obstacles

Lustri

2022

J. Fluid Mech.

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Linearized flow past a submerged obstacle with an elastic sheet resting on the flow surface are studied in the limit that the bending length is small compared to the obstacle depth, in two and three dimensions. Gravitational effects are included in the two-dimensional geometry, but absent in the three-dimensional geometry; the Froude number is chosen so that gravitational and elastic restoring forces are comparable in size. In each of these problems, the waves are exponentially small in the asymptotic limit, and can be computed using exponential asymptotic methods. In the two-dimensional problem, flow past a submerged step is considered. It is found that the relative strengths of the gravitational and elastic restoring forces produce two distinct classes of elastic sheet behaviour. In one parameter regime, constant-amplitude elastic waves and gravity waves extend indefinitely upstream and downstream from the obstacle. In the other parameter regime, all waves decay exponentially away from the obstacle. The equivalent nonlinear two-dimensional geometry is then studied; this asymptotic analysis predicts the existence of a third intermediate regime in which waves persist indefinitely in only one direction, depending on whether the submerged step rises or falls. In the three-dimensional geometry, it is predicted that the elastic waves extend ahead of the submerged source, decaying algebraically in space. The form of these elastic waves is computed, and validated by comparison with numerical computations of the elastic sheet behaviour.

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Section: Introductionmentioning

confidence: 74%

Exponential asymptotics for elastic and elastic-gravity waves on flow past submerged obstacles

Lustri

2022

J. Fluid Mech.

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“…Recent studies on computations of solitary waves by including hydroelasticity in both interface and free surface (see Ref. 39) stimulate us to find steady fall solutions in the same configuration in the future.…”

Section: Discussionmentioning

confidence: 99%

“…In this situation where the elastic plate plays a role as a wave barrier or attenuator, the influence exerted by an obstruction on bottom topography can be important and might need to be considered. Furthermore, it is also mentioned by Pȃrȃu 39 that on the icy moons of Jupiter and Saturn, oceans with layered structures separated by ice shells are hypothesized to exist. Therefore, there has been a growing interest in interfacial hy-draulic waves in a two-layer fluid system.…”

Section: Introductionmentioning

confidence: 99%

Interfacial hydroelastic hydraulic falls and trapped waves over bottom obstacles

Chai

Wang

Părău

2023

Journal of Fluids and Structures

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“…They used a numerical technique to analyze the solitary waves in a stratified fluid. Părău 24 analyzed the hydroelastic solitary waves propagating in a two-layer fluid with two elastic plates. One plate lies on the surface of the fluid whereas the other plate lies between two fluids.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic solitary wave during the head-on collision process in a stratified fluid

Bhatti

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, head-on collision between hydroelastic solitary waves propagating in a two-layer fluid beneath a thin elastic plate is analytically investigated. The plate structure is modeled using the Euler–Bernoulli beam theory with the effect of compressive stress. We consider that the lower- and upper-layer fluids having different constant densities are incompressible, and the motion is irrotational. The asymptotic series solutions of the resulting highly nonlinear coupled differential equations are deduced with the combination of a method of strained coordinates and the Poincaré–Lighthill–Kuo method. The series solutions obtained are presented up to the third-order approximation. The inclusion of all the emerging parameters is discussed graphically and mathematically against interfacial waves, plate deflection, wave speed, phase shift, maximum run-up amplitude, and the velocity functions. The presence of the elastic plate reveals a decreasing impact on the wave profiles in the upper- and lower-layer fluid. However, the distortion profile shows converse behavior in the upper-layer fluid as compared with the lower-layer fluid. Interfacial wave speed also tends to diminish due to the elastic plate parameter and the density ratio as the wave amplitude is high.

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Solitary interfacial hydroelastic waves

Cited by 9 publications

References 27 publications

Exponential asymptotics for elastic and elastic-gravity waves on flow past submerged obstacles

Exponential asymptotics for elastic and elastic-gravity waves on flow past submerged obstacles

Interfacial hydroelastic hydraulic falls and trapped waves over bottom obstacles

Hydroelastic solitary wave during the head-on collision process in a stratified fluid

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