Short and long waves over a muddy seabed

Mei, Chiang C.; Krotov, Mikhael; Huang, Zhenhua; Huhe, Aode

doi:10.1017/s0022112009991923

Cited by 36 publications

(29 citation statements)

References 16 publications

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“…Dalrymple et al 1978;Macpherson 1980;Liu et al 1993;Lin & Jeng 2003) with the correct model in general yet a matter of dispute (Winterwerp & Kesteren 2004). However, under the periodic forcing, a viscoelastic model has been shown to be a very good approximation and is now widely used (Jiang & Mehta 1995;Mei et al 2010). While the general idea presented here can incorporate any mud model, for specificity, we focus our attention on a linear viscoelastic mud model.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of an actuated seafloor-mounted carpet for a high-performance wave energy extraction

Alam

2012

Proc. R. Soc. A.

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It is known that muddy seafloors can extract significant energy from overpassing surface waves via engaging them in strong interaction processes. If a synthetic seabed can respond to the action of surface gravity waves similar to the mud response, then it too can take out a lot of energy from surface waves. Analysis of the performance of a mud-resembling seabed carpet in harvesting ocean wave energy is the subject of this article. Specifically, and on the basis of the field measurements and observations of properties/responses of seafloor mud, we focus our attention on an artificial viscoelastic seabed carpet composed of (vertically acting) linear springs and generators. We show that the system of sea/synthetic-carpet admits two propagating wave solutions: the surface mode and the bottom mode. The damping of a surface-mode wave is proportional to its wavelength and hence is classic. However, the damping of a bottom-mode wave is larger for shorter waves, and is in general stronger than that of the surface-mode wave. To address the effect of (high-order) nonlinear interactions as well as to investigate the performance of our proposed carpet of wave energy conversion (CWEC) against a spectrum of waves, we formulate a direct simulation scheme based on a high-order spectral method. We show, by taking high-order nonlinear interactions into account, that the CWEC efficiency can be significantly higher for steeper waves. We further show that the bandwidth of high performance of the CWEC is broad, it yields minimal wave reflections and its theoretical efficiency asymptotically approaches unity within a finite and (relatively) short extent of deployment.

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Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of an actuated seafloor-mounted carpet for a high-performance wave energy extraction

Alam

2012

Proc. R. Soc. A.

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“…(15) and (16), we find an approximation of horizontal velocity m u : 15) and (16). The governing equation (14) …”

Section: Solutions For the Leading-order Mud Motionmentioning

confidence: 91%

“…For example, Ng and Zhang [3] use the asymptotic approach to study the mass transport induced by waves over a mud layer of the Voigt model. Mei et al [16] even use a generalized viscoelastic model, which can cover most of the linear viscoelastic models. These asymptotic studies of wave-mud interactions are based on sinusoidal waves, in which a complex viscosity of seabed mud is introduced [3,16].…”

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confidence: 99%

“…Mei et al [16] even use a generalized viscoelastic model, which can cover most of the linear viscoelastic models. These asymptotic studies of wave-mud interactions are based on sinusoidal waves, in which a complex viscosity of seabed mud is introduced [3,16]. However, this method for sinusoidal waves cannot be extended to solitary waves, which also appear in the nearshore aera.…”

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confidence: 99%

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The propagation of a solitary wave over seabed mud of the Voigt model

Xia

Zhu

2011

Sci. China Phys. Mech. Astron.

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In shallow water, seabed mud can dissipate the energy of surface gravity waves effectively. In this paper, solitary wave attenuation induced by seabed mud is studied based on a two-layered system, in which the water is assumed to be inviscid and the mud layer is described by the Voigt model. A set of Boussinesq-type equations suitable for solitary waves over the mud of the Voigt model is established, by combining the perturbation analysis and the Laplace transformation. Degenerating into the case of Newtonian model, our Boussinesq-type equations are equivalent to those of Liu and Chan (2007), while the term indicating mud influence is greatly simplified. Based on the equations, the attenuation of solitary waves is studied. An evolution equation of wave amplitude is obtained and the development of mud velocity profiles is discussed. The modal analysis shows that the first mode always dominates mud dynamics. The results are also compared with those of the Maxwell model. solitary wave, seabed mud, wave-mud interaction, Boussinesq-type equations, Voigt model PACS number(s): 47.35.Fg, 47.35.Bb, 47.50.Cd Citation: Xia Y Z, Zhu K Q. The propagation of a solitary wave over seabed mud of the Voigt model.It has been observed that seabed mud can dissipate the energy of surface water waves effectively [1]. As an important mechanism of wave attenuation, the wave-mud interaction has been extensively studied by coastal engineers for decades.The problem of wave-mud interaction is commonly discussed in a two-layered system of water and a muddy seabed. Since water viscosity is very small compared with mud viscosity and makes little contribution to wave attenuation, the water can be treated as an inviscid fluid [2]. Since mud induced wave attenuation is significant only in shallow water, the water layer thickness is often chosen to be small compared with the wave length [2,3].The muddy seabed is a natural cohesive suspension composed of sediment grains and flocs containing minerals and organic matter. Kinds of mud models have been proposed, since the components of mud vary with sites and environments. Jain and Mehta [4] classified basic rheological models of mud according to mud density and the size of solid particles. They pointed out that when seabed sediments are composed of fine suit, the solid particles of the seabed can follow the fluid motion and the entire sediment suspension can be treated as a continuum. These singlephased models are further classified into viscoplastic solid, viscoelastic solid, viscoelastic fluid and viscous fluid according to mud density. For the heaviest mud, viscoplastic solid model is valid, such as the Bingham model [5,6]. For the lightest mud, the viscous fluid model is valid, such as the Newtonian model [2,7-9] and the power-law model [3]. For mud with moderate density, viscoelastic models are widely used, including viscoelastic fluid and viscoelastic solid. Furthermore, viscoelastic models are time-dependent models that describe the response of mud in periodic or transient motions. In these visc...

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“…This is also the case for the wind-wave interaction problem discussed in Section 2. However, for the problems involving two fluids with comparable densities, e.g., interaction between water wave and mud flow (q water /q mud = 0.58 $ 0.95 [34]) and two-layer film flow during coating process (density ratio %1.0 [51,19,20]), the motions of the two fluids are strongly coupled and iteration is thus desired (the effect of density ratio on the two-fluid interaction is discussed in Section 3.2.3).…”

Section: Methodsmentioning

confidence: 99%