The Attenuation of Shallow-Water Waves Over Seabed Mud of a Stratified Viscoelastic Model

Xia, Yuanming

doi:10.1142/s0578563414500211

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…This is granted by the fact that for a linear problem, we only need to introduce a complex viscosity, ν me = ν m + i G m ωρ m with G m being the shear modulus of elasticity, and simply replace ν m by ν me in all our formulations [15,17]. To account for more complex rheological behaviors of mud, the present model can potentially be extended to incorporate the idea of multiple mud layers [28,29], providing that in each single layer, the mud acts as a viscoelastic fluid [22]. The layering structure can also be introduced in the water body if the possible effects of water density stratification are to be considered [30].…”

Section: Discussionmentioning

confidence: 99%

“…With the usual assumptions for water waves, we can define a velocity potential for the motion of water particles as ∇Φ = (u w , w w ), (22) which satisfies the Laplace equation…”

Section: Water Layermentioning

confidence: 99%

“…Due to the diverse rheological properties of fluid mud partly as a consequence of its distinct physico-chemical compositions, it is unequivocal that no single model is capable of describing the entire spectrum of rheological behaviors of fluid mud. Recent analytical results for wave-mud interactions include a depth-integrated model for weakly nonlinear long waves over a thin layer of viscoelastic mud on a mild-slope beach [21], a Boussinesq-type model incorporating two distinct soft mud layers to take into account the vertical variation of mud properties [22], and a linear theory for waves and currents over a viscoud fluid bed [23].…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solution for Wave Scattering by a Surface Obstacle above a Muddy Seabed

Chan

2022

Mathematics

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We present an analytical solution for the scattering of linear progressive waves by a surface rectangular obstacle above a muddy seabed. The bottom cohesive mud is assumed to act as a Newtonian fluid, and the thickness of the mud layer is considered to be comparable to the Stokes boundary layer thickness. Our analytical results based on the matched eigenfunction expansions incorporate the combined effects of obstacles and a fluid mud bottom. By reducing the mud layer thickness or the dimensions of the obstacle to zero, the present study recovers the classical solution for wave scattering by a surface obstacle above a solid bed or wave propagation over a layer of fluid mud. Our analytical predictions of wave amplitudes and wave forces acting on the bottom of the obstacle agree satisfactorily with the available numerical results. The most prominent effect of a muddy seabed is a strong damping of wave amplitude. Parameter study reveals that the obstacle submerged depth, mud layer thickness, and wave frequency can have significant impacts on the attenuation of wave amplitude due to the presence of a muddy seabed.

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Section: Discussionmentioning

confidence: 99%

“…With the usual assumptions for water waves, we can define a velocity potential for the motion of water particles as ∇Φ = (u w , w w ), (22) which satisfies the Laplace equation…”

Section: Water Layermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical Solution for Wave Scattering by a Surface Obstacle above a Muddy Seabed

Chan

2022

Mathematics

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“…Wave-mud interactions have been widely studied in several aspects including wave height attenuation ( [11][12][13]), mud mass transport as the bed load ( [8,9,[14][15][16]] among many others), stratified two-phase flows ( [12,17]), and, suspended load (e.g., the most recent ones are [18,19]). Many analytical and experimental studies have been carried to reveal the unknown aspects of the wave-mud interactions (e.g., wave attenuation and mud mass transport).…”

Section: Introductionmentioning

confidence: 99%

An Analytical Study on Wave-Current-Mud Interaction

Shamsnia

Dutykh

2020

Water

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This study aims at providing analytical investigations to the first and second-order on the wave–current–mud interaction problem by applying a perturbation method. Direct formulations of the wave–current–mud interaction could not be found in the literature. Explicit formulations for the particle velocity, dissipation rates, and phase shift in the first order and the mass transport in the second-order have been obtained. The findings of the current study confirmed that by an increase in the current velocity (e.g., moving from negative to positive values of current velocity), the dissipation rates and mud (instantaneous and mean) velocity decrease. The proposed assumption of a thin mud layer (boundary layer assumption) matches with the laboratory data in the mud viscosity of the orders of (0.01 N/m2) in both wave dissipation and mud mass transport leading to small ranges of discrepancies. The results from the newly proposed model were compared with the measurements and the results of an existing model in the literature. The proposed model showed better agreements in simulating the mud (instantaneous and mean) velocity compared to the existing one.

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Hydroelastic analysis of very large floating structure over viscoelastic bed

Das

Sahoo

2016

Meccanica

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The Attenuation of Shallow-Water Waves Over Seabed Mud of a Stratified Viscoelastic Model

Cited by 9 publications

References 21 publications

Analytical Solution for Wave Scattering by a Surface Obstacle above a Muddy Seabed

Analytical Solution for Wave Scattering by a Surface Obstacle above a Muddy Seabed

An Analytical Study on Wave-Current-Mud Interaction

Hydroelastic analysis of very large floating structure over viscoelastic bed

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