Hydroelasticity and nonlinearity in the interaction between water waves and an elastic wall

2018 ◽  
Vol 845 ◽  
pp. 293-320 ◽  
Author(s):  
Gal Akrish ◽  
Oded Rabinovitch ◽  
Yehuda Agnon
Keyword(s):  
Incident Wave ◽  
Water Waves ◽  
Fundamental Problem ◽  
Wave Force ◽  
Rigid Wall ◽  
High Order ◽  
Dynamical Response ◽  
Computational Domain ◽  
Wave Group ◽  
Elastic Wall

The present study investigates the role of hydroelasticity and nonlinearity in the fundamental problem of the interaction between non-breaking water waves and an elastic wall. To this end, two interaction scenarios are considered: the interaction of a rigid wall supported by springs and a pulse-type wave, and the interaction of an elastic deformable wall and an incident wave group. Both of these scenarios are numerically simulated in a computational domain representing a two-dimensional wave flume. The simplicity of the domain enables one to perform highly efficient simulations using the high-order spectral method (HOSM). Wave generation at the flume entrance and the wave–wall interaction at the flume end are simulated by means of the additional potential concept. In this way, the efficiency that characterizes the original HOSM is preserved for the present non-periodic problems. The investigation of the first scenario reveals the influence of the wall’s dynamical response on the hydrodynamic values. The results show that the maximum wave run-up and wave force are prominently fluctuating around the values corresponding to a fixed wall as a function of the wall’s eigenfrequency, revealing regions of relaxation and amplification. The second scenario studies the effect of the nonlinear evolution of the incident wave group. The high-order wave harmonics generated during the group evolution are found to be significant for predicting extreme hydrodynamic and structural values, and may result in resonant interactions in which hydroelasticity appears to play an important role.

Extreme run-up events on a vertical wall due to nonlinear evolution of incident wave groups

2016 ◽  
Vol 797 ◽  
pp. 644-664 ◽  
Author(s):  
Gal Akrish ◽  
Oded Rabinovitch ◽  
Yehuda Agnon
Keyword(s):  
Nonlinear Wave ◽  
Deep Water ◽  
Incident Wave ◽  
Water Waves ◽  
Nonlinear Evolution ◽  
Vertical Wall ◽  
Computational Domain ◽  
Wave Groups ◽  
Wide Range ◽  
Run Up

Nonlinear evolution of long-crested wave groups can lead to extreme interactions with coastal and marine structures. In the present study the role of nonlinear evolution in the formation of extreme run-up events on a vertical wall is investigated. To this end, the fundamental problem of interaction between non-breaking water waves and a vertical wall over constant water depth is considered. In order to simulate nonlinear wave–wall interactions, the high-order spectral method is applied to a computational domain which aims to represent a two-dimensional wave flume. Wave generation is simulated at the flume entrance by means of the additional potential concept. Through this concept, the implementation of a numerical wavemaker is applicable. In addition to computational efficiency, the adopted numerical approach enables one to consider the evolution of nonlinear waves while preserving full dispersivity. Utilizing these properties, the influence of the nonlinear wave evolution on the wave run-up can be examined for a wide range of water depths. In shallow water, it is known that nonlinear evolution of incident waves may result in extreme run-up events due to the formation of an undular bore. The present study reveals the influence of the nonlinear evolution on the wave run-up in deep-water conditions. The results suggest that extreme run-up events in deep water may occur as a result of the disintegration of incident wave groups into envelope solitons.

scholarly journals MACH-REFLECTION AS A DIFFRACTION PROBLEM

1976 ◽  
Vol 1 (15) ◽  
pp. 45 ◽  
Author(s):  
Udo Berger ◽  
Soren Kohlhase
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Water Waves ◽  
Gas Dynamics ◽  
Mach Reflection ◽  
Diffraction Problem ◽  
Vertical Wall ◽  
Oblique Wave ◽  
Wave Heights ◽  
The Waves

As under oblique wave approach water waves are reflected by a vertical wall, a wave branching effect (stem) develops normal to the reflecting wall. The waves progressing along the wall will steep up. The wave heights increase up to more than twice the incident wave height. The £jtudy has pointed out that this effect, which is usually called MACH-REFLECTION, is not to be taken as an analogy to gas dynamics, but should be interpreted as a diffraction problem.

Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

2014 ◽  
Vol 24 (08) ◽  
pp. 1495-1539 ◽  
Author(s):  
Francesco Bassi ◽  
Lorenzo Botti ◽  
Alessandro Colombo
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Numerical Test ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Element Discretization ◽  
Mesh Free ◽  
Domain Boundaries ◽  
Coarse Grids

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

scholarly journals An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics

2018 ◽  
Vol 848 ◽  
pp. 42-77 ◽  
Author(s):  
L. F. Chen ◽  
J. Zang ◽  
P. H. Taylor ◽  
L. Sun ◽  
G. C. J. Morgan ◽  
...  
Keyword(s):  
High Order ◽  
Quality Data ◽  
Wave Group ◽  
Wave Loading ◽  
Harmonic Force ◽  
Wave Basin ◽  
Wide Range ◽  
Time Histories ◽  
Focused Wave ◽  
Sloping Bed

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$th-harmonic force scales with the $n$th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

scholarly journals SURF SIMILARITY

1974 ◽  
Vol 1 (14) ◽  
pp. 26 ◽  
Author(s):  
J.A. Battjes
Keyword(s):  
Phase Difference ◽  
Incident Wave ◽  
Water Waves ◽  
Slope Angle ◽  
Wave Steepness ◽  
Similarity Parameter ◽  
General Terms ◽  
Depth Ratio ◽  
Run Up ◽  
Set Up

This paper deals with the following aspects of periodic water waves breaking on a plane slope breaking criterion, breaker type, phase difference across the surfzone, breaker height-to-depth ratio, run-up and set-up, and reflection. It is shown that these are approximately governed by a single similarity parameter only, embodying both the effects of slope angle and incident wave steepness. Various physical interpretations of this similarity parameter are given, while its role is discussed m general terms from the viewpoint of model prototype similarity.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

Performance and stability of the double absorbing boundary method for acoustic-wave propagation

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. T59-T72 ◽  
Author(s):  
Toby Potter ◽  
Jeffrey Shragge ◽  
David Lumley
Keyword(s):  
Boundary Layer ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Spectral Response ◽  
Domain Boundary ◽  
Grid Point ◽  
High Order ◽  
Computational Domain ◽  
Absorbing Boundary

The double absorbing boundary (DAB) is a novel extension to the family of high-order absorbing boundary condition operators. It uses auxiliary variables in a boundary layer to set up cancellation waves that suppress wavefield energy at the computational-domain boundary. In contrast to the perfectly matched layer (PML), the DAB makes no assumptions about the incoming wavefield and can be implemented with a boundary layer as thin as three computational grid-point cells. Our implementation incorporates the DAB into the boundary cell layer of high-order finite-difference (FD) techniques, thus avoiding the need to specify a padding region within the computational domain. We tested the DAB by propagating acoustic waves through homogeneous and heterogeneous 3D earth models. Measurements of the spectral response of energy reflected from the DAB indicate that it reflects approximately 10–15 dB less energy for heterogeneous models than a convolutional PML of the same computational memory complexity. The same measurements also indicate that a DAB boundary layer implemented with second-order FD operators couples well with higher-order FD operators in the computational domain. Long-term stability tests find that the DAB and CPML methods are stable for the acoustic-wave equation. The DAB has promise as a robust and memory-efficient absorbing boundary for 3D seismic imaging and inversion applications as well as other wave-equation applications in applied physics.

CFD Analysis of Deck Impact in Irregular Waves: Wave Representation by Transient Wave Groups

2011 ◽  
Author(s):  
O̸ystein Lande ◽  
Thomas B. Johannessen
Keyword(s):  
Wave Field ◽  
Irregular Waves ◽  
Computational Domain ◽  
Cfd Analysis ◽  
Wave Group ◽  
Regular Waves ◽  
Transient Wave ◽  
Wave Groups ◽  
Wave Induced ◽  
Random Background

Analysis of wave structure interaction problems are increasingly handled by employing CFD methods such as the well known Volume-of-Fluid (VoF) method. In particular for the problem of deck impact on fixed structures with slender substructures, CFD methods have been used extensively in the last few years. For this case, the initial conditions have usually been treated as regular waves in an undisturbed wave field which may be given accurately as input. As CFD analyses become more widely available and are used for more complex problems it is also necessary to consider the problem of irregular waves in a CFD context. Irregular waves provide a closer description of the sea surface than regular waves and are also the chief source of statistical variability in the wave induced loading level. In general, it is not feasible to run a long simulation of an irregular seastate in a CFD analysis today since this would require very long simulation times and also a very large computational domain and sophisticated absorbing boundary conditions to avoid build-up of reflections in the domain. The present paper is concerned with the use of a single transient wave group to represent a large event in an irregular wave group. It is well known that the autocovariance function of the wave spectrum is proportional to the mean shape of a large wave in a Gaussian wave field. The transient nature of such a wave ensures that a relatively small wave is generated at the upwave boundary and dissipated at the downwave boundary compared with the wave in the centre of the domain. Furthermore, a transient wave may be embedded in a random background if it is believed that the random background is important for the load level. The present paper describes the method of generating transient wave groups in a CFD analysis of wave in deck impact. The evolution of transient wave groups is first studied and compared with experimental measurements in order to verify that nonlinear transient waves can be calculated accurately using the present CFD code. Vertical wave induced loads on a large deck is then investigated for different undisturbed wave velocities and deck inundations.

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