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1

Impact of nonlinear standing waves underneath a deck

Majewski D., Sulisz W.

Archives of Civil Engineering

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2020

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Vol. 66, nr 4

79--96

EN

A theoretical approach was applied to investigate the impact of nonlinear standing waves underneath a horizontal deck. A solution was achieved by applying a boundary element method. The model was applied to predict impact pressure underneath a deck. The results show that the wave impact is a very complex momentary process. The influence of initial boundary conditions, wave parameters and deck clearance on impact pressure are analysed. The analysis shows that purely sinusoidal waves of very small amplitude may cause an impact pressure several orders of magnitude higher than a pressure arising from typical applications of a linear wave theory. The analysis shows that all these non-intuitive outcomes arise from the complexity of a wave impact process and its enormous sensitivity to initial conditions what indicates serious difficulties in a reliable prediction of a wave impact for complex wave fields or other structures. Laboratory experiments were conducted to validate theoretical results.

PL

Zbadano proces uderzenia nieliniowych, stojących fal wodnych w spód poziomego pokładu. Wykorzystano podejście teoretyczne, którego rozwiązanie opiera się na Metodzie Elementów Brzegowych. Za pomocą modelu wyznaczono ciśnienia generowane uderzeniem fal wodnych. Wyniki wskazują na to, że proces jest bardzo złożony i ma charakter impulsowy. Analizowano wpływ początkowych warunków brzegowych, parametrów fali oraz wysokości zawieszenia pokładu nad powierzchnią spokoju na generowane ciśnienia. Wyniki pokazują, że nawet fale sinusoidalne, o małej amplitudzie mogą wywołać ciśnienia kilkukrotnie większe niż ciśnienia wynikające z typowych zastosowań teorii liniowej falowania. Pokazują również, że często nieintuicyjne wnioski wynikają ze złożoności procesu uderzenia fali i jego dużej czułości na początkowe warunki brzegowe. Wskazuje to na poważne trudności w wiarygodnym modelowaniu procesu uderzenia dla złożonych pól falowych oraz skomplikowanych układów geometrycznych budowli. Przeprowadzono również pomiary laboratoryjne w celu uzyskania danych do walidacji modelu numerycznego. Opracowany model zapewnia wyniki z dokładnością umożliwiającą zastosowanie go w zadaniach inżynierskich.

2

On the SPH Approximations in ModelingWaterWaves

Szmidt K.

Archives of Hydro-Engineering and Environmental Mechanics

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2013

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Vol. 60, nr 1-4

63--86

EN

This paper presents an examination of approximation aspects of the Smoothed Particle Hydrodynamics (SPH) in modeling the water wave phenomenon. Close attention is paid on consistency of the SPH formulation and its relation with a correction technique applied to improve the method accuracy. The considerations are confined to flow fields within finite domains with a free surface and fixed solid boundaries with free slip boundary conditions. In spite of a wide application of the SPH method in fluid mechanics, the appropriate modeling of the boundaries is still not clear. For solid straight line boundaries, a natural way is to use additional (virtual, ghost) particles outside the boundary and take into account mirror reflection of associated field variables. Such a method leads to good results, except for a vicinity of solid horizontal bottoms where, because of the SPH approximations in the description of pressure, a stratification of the fluid material particles may occur. In order to illustrate the last phenomenon, some numerical tests have been made. These numerical experiments show that the solid fluid bottom attracts the material particles and thus, to prevent these particles from penetration into the bottom, a mutual exchange of positions of real and ghost particles has been used in a computation procedure.

3

Finite Difference Analysis of Surface Wave Scattering by Underwater Rectangular Obstacles

Szmidt K.

Archives of Hydro-Engineering and Environmental Mechanics

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2010

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Vol. 57, nr 3-4

179-198

EN

This paper deals with the problem of the scattering of surface water waves by underwater obstacles. The main goal of the investigations is to estimate the efficiency of such structures in protecting sea shelf zones from open sea waves. A useful measure of the protection is the ratio of the square of the amplitude of the transmitted wave to the square of the amplitude of the arriving wave. The problem is formulated in terms of the finite difference method. It is shown that the discrete approach to the problem leads to eigenvalue problems for two matrices resulting from the discrete description. As compared to analytical formulation, the discrete method may be convenient in application to unsteady problems and obstacles of complicated geometry.

4

Wave-induced stresses and liquefaction in seabed according to the biot-type approach

Sawicki A., Mierczyński J.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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Vol. 52, nr 2

131-145

EN

The problem of wave-induced stresses and liquefaction in the seabed according to the Biot-type approach is discussed. The first part of the paper deals with critical analysis of approaches presented in recent literature. It is shown that such approaches do not lead to proper description of the process of wave-induced pore-pressure generation and subsequent liquefaction of seabeds. The second part of this paper deals with the generalisation of the Biot-type approach to the case of shear modulus depending on mean effective stress.

5

Theoretical analysis on experiments in transformation of deep-water-waves

Wilde P.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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Vol. 52, nr 3

213-242

EN

The aim of the paper is to discuss the usefulness of the non-linear Schrödinger differential equation in the study of transformations of progressive deep water waves. Its solution compared with a regular Stokes type wave is essentially restricted to the first order approximation of the second one. The difference is that the Schrödinger equation introduces the concepts of a carrier wave and complex amplitude. In this way the dispersion relation of the third order Stokes expansion is taken into account. The analysis starts with regular, non breaking Stokes waves with large amplitudes as measured in our laboratory. The third order approximation is considered and compared with the corresponding solution of the Schrödinger equation. Then small periodic modifications are introduced in the time series fed into the control system of the generator. The approximation by trigonometric series is applied and the simplified analysis of superposition of very small modifications is used (higher powers of modifications are neglected). The Schrödinger non-linear equation is used in this analysis. The comparison of experimental and calculated envelopes is good, but for the surface elevations in space it is not as good. The approximation by trigonometric series is also applied to study the case of larger modifications. Finally the solutions of the Schrödinger equation corresponding to perfect solitons, are compared with the experimental data for cases where the measured surface elevations look almost like periodic solitons. This gives a reasonable approximation of the real behaviour in a very short space interval. It is not easy to get a good numerical description for the wave problem discussed as the waves are physically unstable. The results of the presented research will be used to establish an effective numerical procedure, stress the approximations introduced by the application of the Schrödinger differential equation and show how the theoretical solutions should be compared with the measured data.

6

On variational formulation in water wave mechanics

Wilde P., Szmidt J. K.

Archives of Hydro-Engineering and Environmental Mechanics

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2004

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Vol. 51, nr 1

55-74

EN

In this paper variational formulations for surface gravitational waves in inviscid incompressible fluids are investigated. The formulations are introduced with the help of the principle of virtual work. The starting point are equations of motion multiplied by a field of virtual displacements and integrated over the region occupied by the fluid. In derivations of the virtual work equation careful attention is paid to mutual relations between Eulerian and Lagrangian descriptions. The integration of the equation with respect to time leads to the expression for the Lagrangian function and then the Hamilton's principle. The case of a potential flow and spatial description provides a generalisation of the Lagrangian given by Luke (1967).

7

"Bottom crystal" and possibility of water wave attenuation

Popov I. Yu

Archives of Mechanics

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2003

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Vol. 55, nr 2

221-232

EN

The influence of periodic bottom structure ("bottom crystal'') on surface water waves is considered. The problem reduces to a two-dimensional Helmholtz operator with periodic potential. Zero-range potential method based on the theory of self-adjoint extensions of symmetric operators is used. It is shown that there is a gap in the spectrum. An application of this spectral property to the problem of wave attenuation is discussed.

8

R-adaptive Trefftz method for steady non-linear water waves

Kołodziej J. A.

Vibrations in Physical Systems

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2002

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Vol. 20

182--183

9

On the generation of water waves in a flume

Wilde P., Wilde M.

Archives of Hydro-Engineering and Environmental Mechanics

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2001

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Vol. 48, nr 4

69-83

EN

The present paper proposes a simple model for the calculation of a time series to control the horizontal motion of the piston of a wavemaker. It is assumed that the initial conditions correspond to water at rest. It is assumed that parameters of kinematics of the fluid (displacement, velocity and acceleration fields) at the initial time are equal to zero. In the first interval the amplitudes grow to an asymptote that corresponds to a regular monochromatic wave. In the second interval the waves decay. Calculated time series were fed in to the control system of our wavemaker and the measured horizontal displacements of the piston compared. The control series was supplemented by terms corresponding to the Stokes type solution by addition of terms with multiples of the basic frequency.

10

Initial boundary value problems for vortex motion of an ideal fluid in bounded domains

Szmidt K.

Archives of Hydro-Engineering and Environmental Mechanics

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2001

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Vol. 48, nr 1

19-33

EN

The paper deals with the problem of vortex motion of an incompressible perfect fluid in bounded domains. The research is confined to chosen cases of steady velocity fields within rectangular, circular and elliptic regions with rigid boundaries. The solution to the initial-value problem of the fluid flow for the assumed velocity fields is the primary object of this paper. It is demonstrated that individual particles of the fluid have their own periods of motion and thus, one should be careful in describing such problems by means of discrete methods, especially in the Lagrangian variables. The problem discussed has its origin in numerical analysis of water waves by means of the finite difference or the finite element method.