scholarly journals A NUMERICAL STUDY OF THE IMPORTANCE OF NONLINEAR EFFECTS FOR FABRY-PEROT RESONANCE OF WATER WAVES

2018 ◽  
pp. 26
Author(s):  
Michel Benoit ◽  
Jie Zhang
Keyword(s):  
Water Waves ◽  
Numerical Study ◽  
Wave Train ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Resonance Phenomenon ◽  
Linear Wave ◽  
Flat Bottom ◽  
Fabry Perot ◽  
Incident Waves

When a regular wave train propagates over a patch of periodic bottom corrugations on an otherwise flat bottom (with still water depth h), the so called Bragg resonance phenomenon can appear, leading to a significant reflection of the incident waves due to the presence of the ripple patch. This effect is maximum when the wavelength of the surface waves (noted A = 2n/k) is twice that of the bottom ripples (noted Ab = 2n/kb). This phenomenon has been studied both experimentally (e.g. Davies & Heathershaw, 1984) and theoretically within the linear wave theory framework (e.g. Mei, 1985; Dalrymple & Kirby, 1986).

Resonant reflection of surface water waves by periodic sandbars

1985 ◽  
Vol 152 ◽  
pp. 315-335 ◽  
Author(s):  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Resonance Condition ◽  
Nonlinear Effects ◽  
Sea Bottom ◽  
Strong Reflection ◽  
Weak Reflection ◽  
Surface Water Waves ◽  
Wave Induced ◽  
Incident Waves ◽  
Resonant Reflection

One of the possible mechanisms of forming offshore sandbars parallel to a coast is the wave-induced mass transport in the boundary layer near the sea bottom. For this mechanism to be effective, sufficient reflection must be present so that the waves are partially standing. The main part of this paper is to explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met. For constant mean depth and simple harmonic waves this resonance has been studied by Davies (1982), whose theory, is however, limited to weak reflection and fails at resonance. Comparison of the strong reflection theory with Heathershaw's (1982) experiments is made. Furthermore, if the incident waves are slightly detuned or slowly modulated in time, the scattering process is found to depend critically on whether the modulational frequency lies above or below a threshold frequency. The effects of mean beach slope are also studied. In addition, it is found for periodically modulated wave groups that nonlinear effects can radiate long waves over the bars far beyond the reach of the short waves themselves. Finally it is argued that the breakpoint bar of ordinary size formed by plunging breakers can provide enough reflection to initiate the first few bars, thereby setting the stage for resonant reflection for more bars.

Dynamic Response of a Porous Seabed and an Offshore Pile to Linear Water Waves

2008 ◽  
Author(s):  
Jian-Fei Lu ◽  
Dong-Sheng Jeng
Keyword(s):  
Dynamic Response ◽  
Water Waves ◽  
Coupled Model ◽  
Expansion Method ◽  
Wave Theory ◽  
Horizontal Displacement ◽  
Element Model ◽  
Wave Force ◽  
Acoustic Medium ◽  
Linear Wave

In this study, a coupled model is proposed to investigate dynamic response of a porous seabed and an offshore pile to ocean wave loadings. Both the offshore pile and the porous seabed are treated as a saturated poro-elastic medium, while the seawater is considered as a conventional acoustic medium. The coupled boundary element model is established by the continuity conditions along the interfaces between the three media. In the system, wave force is considered as an external load and it is evaluated via the wave function expansion method in the context of a linear wave theory. Numerical results show that the increase of the modulus ratio between the pile and the seabed can reduce the horizontal displacement of the pile and the pore pressures of the seabed around the pile. Furthermore, the maximum pore pressure of the seabed usually occurs at the upper part of the seabed around the pile.

Hydroelastic Response of Floating Fuel Storage Modules Placed Side-by-Side

2008 ◽  
Author(s):  
Z. Y. Tay ◽  
C. M. Wang
Keyword(s):  
Numerical Model ◽  
Water Waves ◽  
Plate Theory ◽  
Experimental Tests ◽  
Wave Theory ◽  
Mindlin Plate ◽  
Linear Wave ◽  
Plate Element ◽  
Fuel Storage ◽  
Hydroelastic Response

Presented herein are the hydroelastic responses of two large box-like floating modules that are placed adjacent to each other. These two floating modules form the floating fuel storage facility (FFSF). Owing to the small draft when compared to the length dimensions, the zero-draft assumption is commonly adopted in the modeling of very large floating structures (VLFS) as plates for hydroelastic analysis. However, such an assumption is not applicable to the considered floating modules since the effect of draft on the hydroelastic response is significant when the modules are loaded with fuel. A numerical model taking into account the draft effect is hence developed in order to predict correctly the hydroelastic response and hydrodynamic interactions of floating storage modules placed side-by-side. The floating storage modules are modeled as plates where an improved Mindlin plate element, developed by coupling the reduced integration method and the additional non-conforming modes, is used. Such a plate element does not exhibit spurious modes and shear locking phenomena, thereby making it applicable to both thin and thick plate models. Furthermore, the Mindlin plate theory predicts better stress resultants as compared with its Kirchhoff plate counterpart. The linear wave theory is used to model the water waves. The wave-induced deflections obtained from the numerical model are validated by experimental tests.

Nonlinear effects upon waves near caustics

1979 ◽  
Vol 292 (1392) ◽  
pp. 341-370 ◽  
Keyword(s):  
Water Waves ◽  
Wave Train ◽  
Nonlinear Effects ◽  
Companion Paper ◽  
Exceptional Case ◽  
Wave Intensity ◽  
One Dimensional ◽  
Uniform Medium ◽  
The Waves ◽  
Interpretative Framework

According to linear theory the wave intensity of a slowly varying wave train becomes particularly large near caustics. In this paper it is shown how the waves are modified when the wave intensity is sufficient for nonlinear effects to begin to be important. Two types of near-linear caustics can arise in which nonlinearity either tends to advance or to retard the reflexion of waves from the caustic. General examples are given in terms of one-dimensional wave propagation, and of propagation in a uniform medium. Detailed consideration is given to a particular example: small-amplitude water waves on deep currents. This helps to provide an interpretative framework for the large-amplitude results presented in the companion paper (Peregrine & Thomas 1979). For the more exceptional case of triple roots, or cusped caustics, the increase in wave intensity is even more dramatic. In three appendices the analysis for caustics is extended to some higher-order cases.

A Phase-Amplitude Iteration Scheme for the Optimization of Deterministic Wave Sequences

2009 ◽  
Author(s):  
Christian Schmittner ◽  
Sascha Kosleck ◽  
Janou Hennig
Keyword(s):  
Target Location ◽  
Wave Train ◽  
Target Position ◽  
Wave Theory ◽  
Iteration Scheme ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wave Basin ◽  
Wave Maker ◽  
Phase Amplitude

For the deterministic investigation of extreme events like capsizing, broaching or wave impacts, methods for the generation of deterministic wave sequences are required. These wave sequences can be derived from full scale measurements, numerical simulations or other sources. Most methods for the generation of deterministic wave sequences rely as a backbone on linear wave theory for the backwards transformation of the wave train from the target position in the wave basin to the position of the wave maker. This implies that nonlinear wave effects are not covered to full extend or they are completely neglected. This paper presents a method to improve the quality of the generated wave train via an experimental optimization. Based on a first wave sequence generated with linear wave theory and measured in the wave basin, the phases and amplitudes of the wave maker control signal are modified in frequency domain. The iteration scheme corrects both, shifts in time and in location, resulting in an improved deterministic wave train at the target location. The paper includes results of this method from three different basins with different types of wave generators, water depth and model scales. In addition, this method is applied to a numerical wave tank where the waves can be optimized before the actual basin testing.

Turbulent airflow over water waves-a numerical study

1984 ◽  
Vol 148 ◽  
pp. 225-246 ◽  
Author(s):  
M. A. Al-Zanaidi ◽  
W. H. Hui
Keyword(s):  
Water Waves ◽  
Field Experiments ◽  
Numerical Study ◽  
Wave Train ◽  
Viscous Sublayer ◽  
Smooth Flow ◽  
Fractional Rate ◽  
Wave Phase Velocity ◽  
Turbulent Airflow ◽  
Good Agreement

Turbulent airflow over a Stokes water-wave train of small amplitude is studied numerically based on the two-equation closure model of Saffman & Wilcox (1974) together with appropriate boundary conditions on the wave surface. The model calculates, instead of assuming, the viscous sublayer flow, and it is found that the energy transfer between wind and waves depends significantly on the flow being hydraulically rough, transitional or smooth. Systematic computations have yielded a simple approximate formula for the fractional rate of growth per radian \[ \zeta = \delta_{\rm i}\frac{\rho}{\rho_{\rm w}}\left(\frac{U_{\lambda}}{c}-1 \right)^2, \] with δi = 0.04 for transitional or smooth flow and δi = 0.06 for rough flow, where ρ is density of air, ρw that of water, Uλ wind speed at one wavelength height and c the wave phase velocity. This formula is in good agreement with most existing data from field experiments and from wave-tank experiments. In the case of waves travelling against wind, the corresponding values are δi = −0.024 for transitional and smooth flow, and δi = −0.04 for rough flow.

scholarly journals TRANSMISSION OF REGULAR WAVES PAST FLOATING PLATES

1974 ◽  
Vol 1 (14) ◽  
pp. 112
Author(s):  
Uygur Sendil ◽  
W.H. Graf
Keyword(s):  
Water Depth ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Regular Waves ◽  
Transmission Coefficients ◽  
Wave Flume ◽  
Wave Heights ◽  
Incident Waves

Theoretical solutions for the transmission beyond and reflection of waves from fixed and floating plates are based upon linear wave theory, as put forth by John (1949), and Stoker (1957), according to which the flow is irrotational, the fluid is incompressible and frictionless, and the waves are of small amplitude. The resulting theoretical relations are rather complicated, and furthermore, it is assumed that the water depth is very small in comparison to the wave length. Wave transmissions beyond floating horizontal plates are studied in a laboratory wave flume. Regular (harmonic) waves of different heights and periods are generated. The experiments are carried out over a range of wave heights from 0.21 to 8.17 cm (0.007 to 0.268 ft), and wave periods from 0.60 to 4.00 seconds in water depth of 15.2, 30.5, and 45.7 cm (0.5, 1.0 and 1.5 ft). Floating plates of 61, 91 and 122 cm (2, 3 and 4 ft) long were used. From the analyses of regular waves it was found that: (1) the transmission coefficients, H /H , obtained from the experiments are usually less than those obtained from the theory. This is due to the energy dissipation by the plate, which is not considered in the theory. (2) John's (1949) theory predicts the transmission coefficients, H /H , reasonably well for a floating plywood plate, moored to the bottom and under the action of non-breaking incident waves of finite amplitude. (3) a floating plate is less effective in damping the incident waves than a fixed plate of the same length.

A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part II: Finite size effects

2019 ◽  
Vol 72 (3) ◽  
pp. 387-414
Author(s):  
R I Brougham ◽  
I Thompson
Keyword(s):  
Size Effects ◽  
Water Waves ◽  
Direct Method ◽  
Finite Size ◽  
Wave Theory ◽  
Bloch Wave ◽  
General Context ◽  
Linear Wave ◽  
Finite Size Effects ◽  
Scatterer Size

Summary A method for determining the reflection and transmission properties of a periodic structure occupying a half-space, previously developed for lattices formed from point scatterers, is generalized to allow for finite size effects. This facilitates the consideration of much higher frequencies (or more precisely, much higher scatterer size to wavelength ratios), and also a wider range of boundary conditions. The method is presented in a general context of linear wave theory, and physical interpretations are given for acoustics, elasticity, electromagnetism and water waves.

In-Line Forces on Vertical Cylinders in Deepwater Waves

1985 ◽  
Vol 107 (1) ◽  
pp. 18-23
Author(s):  
T. H. Dawson
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Wave Theory ◽  
Stokes Wave ◽  
Wave Forces ◽  
Linear Wave ◽  
Random Waves ◽  
Morison Equation ◽  
Circular Particle ◽  
Wave Cycle

Laboratory measurements of the total in-line forces on a fixed vertical 2-in-dia cylinder in deep-water regular and random waves are given and compared with predictions from the Morison equation. Results show, for regular waves with heights ranging from 2 to 22 in. and frequencies ranging from 0.4 to 0.9 Hz that the Morison equation, with Stokes wave theory and constant drag and inertia coefficients of 1.2 and 1.8, respectively, provides good agreement with the measured maximum wave forces. The force variation over the entire wave cycle is also well represented. The linearized Morison equation, with linear wave theory and the same coefficients likewise provides close agreement with the measured rms wave forces for irregular random waves having approximate Bretschneider spectra and significant wave heights from 5 to 14 in. The success of the constant-coefficient approximation is attributed to a decreased dependence of the coefficients on dimensionless flow parameters as a result of the circular particle motions and large kinematic gradients of the deep-water waves.

scholarly journals Nonlinear diffraction of water waves by offshore stuctures

1986 ◽  
Vol 9 (4) ◽  
pp. 625-652 ◽  
Author(s):  
Matiur Rahman ◽  
Lokenath Debnath
Keyword(s):  
Water Waves ◽  
Current Knowledge ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Resonance Phenomenon ◽  
Polar Coordinates ◽  
Wave Forces ◽  
Water Wave Problem ◽  
Nonlinear Diffraction ◽  
Conical Structures

This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear) effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.

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