Progressive Waves in Real Fluids Over a Rigid Permeable Bottom

The linear wave theory and the nonlinear-unsteady porous flow model are applied to analyze the energy dissipation and the bed pore water pressure induced by the interaction of wave, uniform current and porous bottom without considering the nonlinear waves and the viscosity effect inside the boundary layer. In this model, the linear, inertial and turbulent resistances are combined into a linearized resistance coefficient and the present system can be analyzed by a linear boundary value problem. The numerical result is quite agreement with the existing experimental data. It shows that the energy dissipation is reduced by the Doppler shift and the distribution of energy loss moves to the lower relative water depth region in the wave-following current. On the other hand, the bed pore water pressure in the wave-following current is always lager than that in the pure wave and the wave-opposing current.Keywords：wave-current interaction, rigid porous medium, nonlinear-unsteady porous flow model, energy dissipation 1.IntroductionThe Doppler shift is the relative motion which is the change in the frequency of waves for an observer moving relative to the source. In the water wave, it represents the wave-current interaction. Non-uniform or uniform currents influence the characteristics of waves. The speed and wavelength are increased in waves encountering a favorable current and vice verse for the opposing current (Nielsen, 2012).A lot of theoretical and experimental studies for wave-varying current interaction in the infinite and finite water depth with the smooth impermeable seabed had been performed. Typical samples are found in Stewart(1960,1961), Jonsson et al.(1970Jonsson et al.( ,1978, Jonsson(1977), Peregrine(1976), Thomas(1981Thomas( ,1990, Baddourand Song (1990), Groeneweg and Battjes (2003) (2013, 2014) used the perturbation approach to analyze the high-order nonlinear wave-current interaction in 3D Lagrangian scheme, and the mass transport velocity and the particle orbit both were measured in the 1D wave-current tank. In the laboratory experiment (Huang et al.,1972), it displayed the relative importance of wave-current interaction is decided by the nondimensional parameter 0 / U C with U as the current velocity and 0 C the wave speed without the current. The kinematics of the strong interaction in the wave-current motion were measured by Lai et al.(1989). Their results confirmed the critical 0 / U C with the currents induced the blockage of waves is -0.25. Soares and Pablo (2006) carried out an experimental study for the wave-current motion, and determined the change of wave spectra due to the coexistence of wave-current in the 3D wave basin. The experimental results showed that the energy absorbed by waves in the opposing current is impossible to continue the growth, and it is up to a certain limit, eventually resulting in wave breaking. However, the porous seabed and the energy dissipation are not considered in there existing studies.The experiment for the wave-current interaction over a rough bed was perfo...

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“…(9)~(10) can be determined by applying boundary conditions eqs. (11)~(15) (Dean and Dalrymple, 1991;Chen et al,2010), …”

Section: Complex Dispersion Relationshipmentioning

confidence: 99%

Energy Dissipation of Wave-Uniform Current Over a Rigid Porous Media With Finite Thickness

Lin

Hsu

Yu³

et al. 2014

Int. Conf. Coastal. Eng.

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“…Such expensive losses made them think that security of underwater equipment and the influence of internal gravity waves should be controlled. The internal waves characteristics are used for appreciation of their influence on the environment and underwater platforms of oil and gas deposits at the shelf (Arctic basin, China and Yellow Seas, etc) [4][5][6][7][8][9][10][11][12]. Special interest to research of internal gravity waves is connected with also intensive exploitation of Arctic and its natural wealth.…”

Section: Introductionmentioning

confidence: 99%

Asymptotical analysis of internal gravity wave dynamics in stratified medium

Булатов¹,

Vladimirov²

2014

ams

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In the paper taking the assumption of the slowness of the change of the parameters of the vertically stratified medium in the horizontal direction and in time, the evolution of the non-harmonic wave packages of the internal gravity waves has been analyzed. The concrete form of the wave packages can be expressed through some model functions and is defined by the local behavior of the dispersive curves of the separate modes near to the corresponding special points. The solution of this problem is possible with the help of the modified variant of the special-time ray method offered by the authors (the method of geometrical optics), the basic difference of which consists that the asymptotic representation of the solution may be found in the form the series of the non-integer degrees of some small parameter. At that the exponent depends on the concrete form of representation of this package. The obvious kind of the representation is determined from the principle of the localness and the asymptotic behavior of the solution in the stationary and the horizontallyhomogeneous case. The phases of the wave packages are determined from the corresponding equations of the eikonal, which can be solved numerically on the characteristics (rays). Amplitudes of the wave packages are determined from the laws of concervation of the some invariants along the characteristics (rays).

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“…Several studies (Chen et al, 2010;Liu et al, 1996;Sparrow et al, 2012) have proved that a permeable bed has a significant effect on the structure of the boundary layer above the bed with the horizontal velocities, turbulence and shear stress all being affected. However, the potential causes of this phenomenon have not been thoroughly investigated.…”

Section: Introductionmentioning

confidence: 99%

Briefing: Young Coastal Scientists and Engineers Conference 2013

Murray¹,

Thorne²,

Bremer³

et al. 2014

Proceedings of the Institution of Civil Engineers - Maritime En

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On 25–26 March 2013, 52 early career scientists and engineers, studying various aspects of coastal science, met at the University of Aberdeen for the ninth Young Coastal Scientists and Engineers Conference. The conference was jointly organised by the School of Engineering, University of Aberdeen, and Marine Scotland Science. Early-career scientists, researchers and practitioners presented 23 oral and 17 poster presentations over the 2-day meeting. The papers all had a coastal theme with a large diversity in the subjects covered, including waves, currents, tidal energy, coastal erosion, sediment transport, fluid mechanics and particle tracking. This briefing paper reports on the conference, and presents the keynote lecture and four papers voted to be of especially high quality by the panel of judges.

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Progressive Waves in Real Fluids Over a Rigid Permeable Bottom

Cited by 10 publications

References 16 publications

Energy Dissipation of Wave-Uniform Current Over a Rigid Porous Media With Finite Thickness

Energy Dissipation of Wave-Uniform Current Over a Rigid Porous Media With Finite Thickness

Asymptotical analysis of internal gravity wave dynamics in stratified medium

Briefing: Young Coastal Scientists and Engineers Conference 2013

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