The Harmonic Structure of the Focused Wave in a Wave Flume

2021 ◽  
Author(s):  
Huixing Gao ◽  
Jianjun Zhou ◽  
Yang Song ◽  
Qinghe Fang
Keyword(s):  
Wave Theory ◽  
Higher Order ◽  
Stokes Wave ◽  
Wave Group ◽  
Harmonic Structure ◽  
Extreme Waves ◽  
Third Order ◽  
Wave Flume ◽  
Wave Elevation ◽  
Focused Wave

Abstract In recent years, extreme waves have attracted more and more attention due to its threat to offshore and coastal structures. It is essential to obtain further insight into the formation and propagation of the extreme waves. The formation of extreme waves mainly comes from the simultaneous focusing of wave group energy in the ocean. In the present study, the nonlinear characteristics of the extreme wave are experimentally investigated by the wave focusing method. The phase decomposition methods, both two-phases separation and four-phases separation methods, are used to obtain the higher harmonic elevation in the focused wave. The results show that the four-phases separation method can reasonably extract the first four harmonics. With the separated results, the nonlinear analysis of the wave elevation and velocity of the focused wave is carried out. It is found that the harmonics of the wave group focused at the same time, but the wave elevation and energy of higher-order harmonics are smaller than that of the overall wave. The Stokes wave theory can describe the variation of second-order harmonics satisfactorily. However, the Stokes wave theory cannot estimate third-order harmonics accurately. More work should be carried out to figure out the third-order wave interaction occurring during wave focusing. With a distributed wave gauge system, the wave evolution along the wave flume is measured. The evanescent modes significantly influence the wave group’s harmonic structure near the wavemaker. The coefficients of the higher-order harmonics are obtained from the measured elevations. The nonlinear wave elevation of the focused wave can be reconstructed with those coefficients basing on the linear theoretical solution, which is in good agreement with the experimental results.

Estimates of Wave Elevations Around Structures

2010 ◽  
Author(s):  
Anne Katrine Bratland ◽  
Ragnvald Bo̸rresen ◽  
Per Ivar Barth Berntsen
Keyword(s):  
Water Depth ◽  
Wave Theory ◽  
Higher Order ◽  
Offshore Platforms ◽  
Test Results ◽  
Regular Wave ◽  
First Order ◽  
Wave Elevation ◽  
Higher Order Terms ◽  
Wave Elevations

When designing offshore platforms the still water air gap has to be large enough to avoid major wave-in-deck impact. Since wave elevation in harsh weather is highly non-linear, corrections to the calculated first order solution are necessary. The present method is a pragmatic approach to estimate the higher order contributions, utilizing the first order response amplitude operator and higher order wave elevations. For infinite water depth it is shown that regular wave theory is a good approximation for calculating second order wave elevation in irregular seas. So the higher order waves are calculated with regular wave theory, and the QTF and higher order terms are approximated by the first order RAO. Comparison with model test results have been performed for a GBS in moderate water depth and a semi-submersible is relatively deep water. The agreements with model tests are satisfactory.

scholarly journals Wave-Generated Current: A Second-Order Formulation

2020 ◽  
Vol 8 (6) ◽  
pp. 418
Author(s):  
Anne Katrine Bratland
Keyword(s):  
Wave Theory ◽  
Second Order ◽  
Stokes Drift ◽  
Wave Number ◽  
Stokes Wave ◽  
Wave Loads ◽  
Third Order ◽  
The Third ◽  
Computational Fluid Dynamics Cfd ◽  
The Mean

In Stokes’ wave theory, wave numbers are corrected in the third order solution. A change in wave number is also associated with a change in current velocity. Here, it will be argued that the current is the reason for the wave number correction, and that wave-generated current at the mean free surface in infinite depth equals half the Stokes drift. To demonstrate the validity of this second-order formulation, comparisons to computational fluid dynamics (CFD) results are shown; to indicate its effect on wave loads on structures, model tests and analyses are compared.

On higher-order wave theory for submerged two-dimensional bodies

1969 ◽  
Vol 38 (2) ◽  
pp. 415-432 ◽  
Author(s):  
Nils Salvesen
Keyword(s):  
Free Surface ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Drag ◽  
Higher Order ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
Free Surface Waves ◽  
Body Shapes

The importance of non-linear free-surface effects on potential flow past two-dimensional submerged bodies is investigated by the use of higher-order perturbation theory. A consistent second-order solution for general body shapes is derived. A comparison between experimental data and theory is presented for the free-surface waves and for the wave resistance of a foil-shaped body. The agreement is good in general for the second-order theory, while the linear theory is shown to be inadequate for predicting the wave drag at the relatively small submergence treated here. It is also shown, by including the third-order freesurface effects, how the solution to the general wave theory breaks down at low speeds.

scholarly journals Eulerian–Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry

2012 ◽  
Vol 370 (1964) ◽  
pp. 1687-1702 ◽  
Author(s):  
Motohiko Umeyama
Keyword(s):  
Particle Image Velocimetry ◽  
Vector Fields ◽  
Particle Image ◽  
Taylor Series Expansion ◽  
Wave Theory ◽  
Stokes Wave ◽  
Lagrangian Analysis ◽  
Wave Flume ◽  
Image Velocimetry ◽  
Wave Cycle

This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an Eulerian scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the Eulerian velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.

Multi-Focused Wave Groups in Wave Flume

2019 ◽  
Author(s):  
Qinghe Fang ◽  
Cunbao Zhao ◽  
Anxin Guo
Keyword(s):  
Irregular Waves ◽  
Frequency Resolution ◽  
Random Wave ◽  
Wave Group ◽  
Wave Groups ◽  
Large Wave ◽  
Wave Flume ◽  
Space And Time ◽  
Focused Wave ◽  
Focused Wave Group

Abstract People can simulate extreme hydrodynamic conditions in a laboratory facility by interfering a numbers of regular waves at a certain point in space and time, which is focused wave. It is obviously higher and steeper than any other wave, e.g. regular or irregular waves, within the propagating wave group. The focused wave occurs at a designed point both in space and time. It represents an event with a large return period which would take a long time to reproduce within a random wave sequence. The focused wave, representing of a large wave occurring in a random sea, is quite frequently used to investigate wave loading on marine or coastal structures. However, most research only employ one single focused wave group. Taking the randomness of the wave-structure interaction, repeated tests would be suggested by some textbooks or codes to eliminate the odd results. However, it would take more time to conduct those tests no matter in the laboratory or in the numerical simulations. In our present work, we use a novel method to experimentally generate several focused wave group with different focus time but same focus point at the same time to obtain multi-focused wave groups. The wave elevation and water particle kinematics are measured. The influence of peak frequency, frequency resolution and period of focused wave group are checked and discussed. The results show that present method can generate stable and repeatable focused wave groups in the wave flume.

A Note on the Evaluation of the Wave Resistance of Two-Dimensional Bodies from Measurements of the Downstream Wave Profile

1983 ◽  
Vol 27 (02) ◽  
pp. 90-92
Author(s):  
James H. Duncan
Keyword(s):  
Wave Train ◽  
Wave Theory ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Third Order ◽  
The Subject ◽  
Lord Kelvin ◽  
The Waves ◽  
The Vertical Distribution

As a body moves horizontally at constant speed in the proximity of a free surface it experiences a resistance due to the generation of waves. In two-dimensional cases the determination of this resistance from properties of the wave train has been the subject of several investigations. The linear theory was first presented by Lord Kelvin [1] 2 and later by Havelock [2] and Lamb [8]. Wehausen and Laitone [4] have derived an exact resistance formula in terms of the vertical distribution of velocity in the waves and the downstream surface height profile. This formula was later evaluated by Salvesen and von Kerczek [5] using third-order Stokes wave theory.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

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.

Square-root-like higher-order topological states in three-dimensional sonic crystals

2021 ◽  
Author(s):  
Zhiguo Geng ◽  
Huanzhao Lv ◽  
Zhan Xiong ◽  
Yu-Gui Peng ◽  
Zhaojiang Chen ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Higher Order ◽  
Square Root ◽  
Root Lattice ◽  
Third Order ◽  
Topological Materials ◽  
Topological States ◽  
Sonic Crystal ◽  
Sonic Crystals

Abstract The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at the K-H direction induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in the z direction. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty

2020 ◽  
Vol 19 (04) ◽  
pp. 2050038
Author(s):  
Keqiang Dong ◽  
Xiaofang Zhang
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Higher Order ◽  
Stationary Time Series ◽  
Residual Entropy ◽  
Third Order ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual ◽  
Simulated Time ◽  
Analyze Time Series

The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated time series generated by uniform distribution on [0, 1]. Finally, we present the application of higher-order multiscale fractional cumulative residual entropy in logistic map time series and stock markets time series, respectively.

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