scholarly journals A Nonlinear Coupled-Mode Model for Waves Propagating in Vertically Sheared Currents in Variable Bathymetry—Collinear Waves and Currents

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 61 ◽  
Author(s):  
Kostas Belibassakis ◽  
Julien Touboul
Keyword(s):  
Wave Scattering ◽  
Bottom Topography ◽  
Coupled System ◽  
Continuity Condition ◽  
Present System ◽  
Coupled Mode ◽  
Bottom Boundary Condition ◽  
Non Linear ◽  
Waves And Currents ◽  
Current Interaction

A novel coupled-mode model is developed for the wave–current–seabed interaction problem, with application in wave scattering by non-homogeneous, sheared currents over general bottom topography. The formulation is based on a velocity representation defined by a series of local vertical modes containing the propagating and evanescent modes, able to accurately treat the continuity condition and the bottom boundary condition on sloping parts of the seabed. Using the above representation in Euler equations, a coupled system of differential equations on the horizontal plane is derived, with respect to the unknown horizontal velocity modal amplitudes. In the case of small-amplitude waves, a linearized version of the above coupled-mode system is obtained, and the dispersion characteristics are studied for various interesting cases of wave–seabed–current interaction. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system is reduced to a one-equation, non-linear model, generalizing Boussinesq models. The analytical structure of the present coupled-mode system facilitates extensions to treat non-linear effects and further applications concerning wave scattering by inhomogeneous currents in coastal regions with general 3D bottom topography.

A Weakly Nonlinear Coupled-Mode Model for Wave-Current-Seabed Interaction Over General Bottom Topography

2008 ◽  
Author(s):  
K. A. Belibassakis ◽  
Th. P. Gerostathis ◽  
G. A. Athanassoulis
Keyword(s):  
Horizontal Plane ◽  
Bottom Topography ◽  
Additional Term ◽  
Scattered Wave ◽  
Present System ◽  
Weakly Nonlinear ◽  
Coupled Mode ◽  
Wave Potential ◽  
Seabed Interaction ◽  
Interaction Problem

A weakly nonlinear, coupled-mode model is developed for the wave-current-seabed interaction problem, with application to wave scattering by steady currents over general bottom topography. Based on previous work by the authors (Athanassoulis & Belibassakis [1], Belibassakis et al [2]), the vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus an additional term accounting for the bottom boundary condition when the bottom slope is not negligible. Using the above representation, in conjunction with Luke’s [3] variational principle, the wave-current-seabed interaction problem is reduced to a coupled system of differential equations on the horizontal plane. If only the propagating mode is retained in the vertical expansion of the wave potential, and after simplifications, the present system is reduced to an one-equation model compatible with Kirby’s [4] mild-slope model with application to the problem of wave-current interaction over slowly varying topography. The present coupled-mode system is discretized on the horizontal plane by using a second-order finite difference scheme and numerically solved by iterations. Numerical results are presented for two representative test cases, demonstrating the importance of the first evanescent modes and the sloping-bottom mode. The analytical structure of the present model facilitates its extension to treat fully non-linear waves, and it can be further elaborated to study wave propagation over random bottom topography and general currents.

Numerical Modeling of Seabed Response to Combined Wave-Current Loading

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
J.-S. Zhang ◽  
Y. Zhang ◽  
C. Zhang ◽  
D.-S. Jeng
Keyword(s):  
Numerical Modeling ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Laboratory Measurements ◽  
Navier Stokes Equations ◽  
Closure Scheme ◽  
Waves And Currents ◽  
Current Interaction ◽  
Wave Maker ◽  
Current Loading

In this paper, a numerical model is developed to study the dynamic response of a porous seabed to combined wave-current loadings. While the Reynolds-averaged Navier–Stokes equations with k-ε turbulence closure scheme and internal wave-maker function are solved for the phenomenon of wave-current interaction, Biot's poro-elastic “u-p” model is adopted for the seabed response. After validated by the laboratory measurements, this model is applied for the investigation of the effects of waves and currents on the wave-current induced pore pressures. Furthermore, the effects of currents on maximum liquefaction depths of a porous seabed is examined, and it is concluded that the opposite currents will increase the liquefaction depth up to 30% of that without currents.

Flexural Gravity Wave Scattering Due to Variations in Bottom Topography

2009 ◽  
Author(s):  
D. Karmakar ◽  
J. Bhattacharjee ◽  
T. Sahoo
Keyword(s):  
Gravity Wave ◽  
Water Waves ◽  
Wave Scattering ◽  
Bottom Topography ◽  
Single Step ◽  
Energy Relation ◽  
Wide Spacing ◽  
Expansion Formulae ◽  
Flexural Gravity Wave ◽  
Multiple Step

Oblique flexural gravity wave scattering due to abrupt change in bottom topography is investigated under the assumption of linearized theory of water waves. The problem is studied first for single step in case of finite water depth whose solution is obtained based on the expansion formulae for flexural gravity wavemaker problem and corresponding orthogonal mode-coupling relation. The results for the multiple step topography are obtained from the result of single step using the method of wide-spacing approximation. Energy relation for oblique flexural gravity wave scattering due to change in bottom topography is used to check the accuracy of the computation. Using shallow water approximation the wave scattering due to multiple step topography is derived considering the continuity of mass and energy flux. In this case also the result for single step topography is obtained and then using the wide-spacing approximation the result for multiple steps are derived. Numerical results for reflection and transmission coefficients and deflection of ice sheet are obtained to analyze the effect of multiple step topography on the propagation of flexural gravity waves.

Effect of bottom topography on wave scattering by multiple porous barriers

Meccanica ◽  
2017 ◽  
Vol 53 (4-5) ◽  
pp. 887-903 ◽  
Author(s):  
R. B. Kaligatla ◽  
S. Tabssum ◽  
T. Sahoo
Keyword(s):  
Wave Scattering ◽  
Bottom Topography ◽  
Porous Barriers

An Influence of Shroud Design on the Dynamic and Aeroelastic Behavior of Bladed Disc Assemblies

1997 ◽  
Author(s):  
G. Jacquet-Richardet ◽  
F. Moyroud ◽  
T. H. Fransson
Keyword(s):  
Mode Shape ◽  
Coupled System ◽  
Frequency Mode ◽  
Reduced Model ◽  
Interface Plane ◽  
Model Based ◽  
Non Linear

Precise non-linear aeroelastic modeling of shrouded bladed-disc assemblies is generally beyond present capacities and analyses often assume that the behavior of the coupled system remains linear and retains a cyclic symmetrical property. In this paper, several models of shrouded assemblies, in the particular case of fully slipping interfaces, are examined and compared. Considering the cyclic symmetrical property of the structure, only the model where shroud segments can slip and propagation relations are applied in the direction normal to the interface plane, should be used. A reduced model based on a direct discretisation of the whole assembly is presented and validated. The application is based on a first stage shrouded fan. The influence of varying the interface shroud angle is examined in terms of frequency, mode shape and aeroelastic damping.

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