Second Order Wave Propagating Along VLFS

2019 ◽  
Author(s):  
Kazuhiro Iijima ◽  
Chong Ma
Keyword(s):  
Nonlinear Wave ◽  
Boundary Surface ◽  
Finite Amplitude ◽  
Stokes Wave ◽  
Linear Wave ◽  
Frequency Range ◽  
Floating Structure ◽  
One Dimensional ◽  
Free Surface Wave ◽  
Nonlinear Free Surface

Abstract This paper addresses the nonlinear deflection wave which propagates along a Very Large Floating Structure (VLFS). The whole VLFS is modeled as a one-dimensional beam afloat on the water surface in a vertical two-dimensional plane. It is assumed that the deflection of the wave propagating along the VLFS has a finite amplitude. The nonlinear wave propagating along the VLFS is investigated by extending the propagation theory of the linear wave along the VLFS. The kinetic and kinematic conditions at the boundary surface between the water and VLFS are considered rigorously up to the 2nd order. The 2nd order wave is obtained as a wave associated with the 1st order wave. The characteristics of the nonlinear wave along the VLFS are elucidated by the mathematical solution. The nonlinear wave along the VLFS has characteristics slightly different from the nonlinear free surface wave, known as Stokes wave. The positive peak of the wave along the VLFS is higher than the negative peak due to the nonlinearity in some frequency range while it is the opposite in the other frequency range. The amplitude of the 2nd order wave increases divergently at the frequency range between the two frequency regimes.

Crest-Height Distribution in Nonlinear Random Wave

2009 ◽  
Author(s):  
Cuilin Li ◽  
Dingyong Yu ◽  
Yangyang Gao ◽  
Junxian Yang
Keyword(s):  
Nonlinear Wave ◽  
Wave Theory ◽  
Distribution Functions ◽  
Theoretical Distribution ◽  
Distribution Model ◽  
Stokes Wave ◽  
Wave Crest ◽  
Linear Wave ◽  
Height Distribution ◽  
Crest Height

Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement. With the development of ocean exploitation, waves crest heights represent a key point in the design of coastal structures, both fixed and floating, for shoreline protection and flood prevention. Waves crest height is the dominant parameter in assessing the likelihood of wave-in-deck impact and its resulting severe damage. Unlike wave heights, wave crests generally appear to be affected by nonlinearities; therefore, linear wave theory could not be satisfied to practical application. It is great significant to estimate a new nonlinear wave crest height distribution model correctly. This paper derives an approximation distribution formula based on Stokes wave theory. The resulting theoretical forms for nonlinear wave crest are compared with observed data and discussed in detail. The results are shown to be in good agreement. Furthermore, the results indicate that the new theoretical distribution has more accurate than other methods presented in this paper (e.g. Rayleigh distribution and Weibull distribution) and appears to have a greater range of applicability.

scholarly journals COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL

1988 ◽  
Vol 1 (21) ◽  
pp. 42
Author(s):  
Thomas A. Hardy ◽  
Nicholas C. Kraus
Keyword(s):  
Nonlinear Refraction ◽  
Wave Model ◽  
Wave Theory ◽  
Quantitative Agreement ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Second Order ◽  
Stokes Wave ◽  
Linear Wave ◽  
Cnoidal Wave

An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.

scholarly journals 1D Numerical Study of Nonlinear Propagation of Finite Amplitude Waves in Traveling Wave Tubes with Varying Cross Section

2020 ◽  
Vol 25 (1) ◽  
pp. 88-95
Author(s):  
Zhineng Zhang ◽  
Ling Zheng ◽  
Tingfei Yan ◽  
Yao Wu
Keyword(s):  
Nonlinear Wave ◽  
Traveling Wave ◽  
Sound Pressure ◽  
Acoustic Pressure ◽  
Finite Amplitude ◽  
Nonlinear Propagation ◽  
Traveling Wave Tube ◽  
Wave Tube ◽  
One Dimensional ◽  
Waveform Distortion

The nonlinear acoustic problem of a finite amplitude plane wave propagating along the axial direction in a traveling wave tube is studied. Based on the one-dimensional Westervelt equation, a one-dimensional nonlinear wave equation is derived in which the cross section of the traveling wave tube is considered. The two-order finite difference scheme is used to solve the nonlinear wave equation. The nonlinear propagation characteristics of a finite amplitude wave in the traveling wave tube is analyzed. In the expanding transition section, the acoustic pressure amplitude of the acoustic wave decreases with the increase of the cross-sectional area of the pipeline. The nonlinear characteristics of the acoustic wave show waveform distortion and harmonic growth. The waveform distortion becomes more serious in the rear of traveling wave tube than in the front of the tube. Considering the acoustic reflection condition at the mouth, the influence of differently shaped diffusion sections on the acoustic pressure distribution in the test section is investigated. The larger the change rate of the diffusion section in an area, the less amplitude of the sound pressure, and the nonlinear effect of the sound wave propagation is weakened. These nonlinear wave propagation characteristics in a travelling wave tube provide important guidance for both designing a uniform sound pressure distribution in the test section and determining the optimal measuring points for different sizes of structures in spacecraft.

Effect of Double Defects on Transmission Spectra of One-Dimensional Photonic Crystals

2010 ◽  
Vol 663-665 ◽  
pp. 725-728 ◽  
Author(s):  
Yuan Ming Huang ◽  
Qing Lan Ma ◽  
Bao Gai Zhai ◽  
Yun Gao Cai
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Theoretical Calculations ◽  
Stop Band ◽  
Band Gaps ◽  
Characteristic Matrix ◽  
Frequency Range ◽  
Defect Band ◽  
One Dimensional ◽  
The One

Considered the model of the one-dimensional photonic crystals (1-D PCs) with double defects, the refractive indexes (n2’, n3’ and n2’’, n3’’) of the double defects were 2.0, 4.0 and 4.0, 2.0 respectively. With parameter n2=1.5, n3=2.5, by theoretical calculations with characteristic matrix method, the results shown that for a certain number (14 was taken) of layers of the 1-D PCs, when the double defects abutted, there was a defect band gap in the stop band gap, while when the double defects separated, there occurred two defect band gaps in the stop band gap; besides, with the separation of the two defects, the transmittance of the double defect band gaps decreased gradually. In addition, in this progress, the frequency range of the stop band gap has a little increase from 0.092 to 0.095.

Peculiarities of linear wave interaction with nonlinear media interface

2018 ◽  
Vol 32 (30) ◽  
pp. 1850371 ◽  
Author(s):  
S. E. Savotchenko
Keyword(s):  
Guided Waves ◽  
Mathematical Formulation ◽  
Wave Interaction ◽  
Linear Wave ◽  
Stationary Waves ◽  
One Dimensional ◽  
Nonlinear Properties ◽  
Dimensional Boundary ◽  
Nonlinear Interface ◽  
Plane Defect

We analyze guided waves in the linear media separated nonlinear interface. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The Kerr type nonlinearity in the equation is taken into account only inside the waveguide. We show that the existence of nonlinear stationary waves of three types is possible in defined frequency ranges. We derive the frequency of obtained stationary states in explicit form and find the conditions of its existence. We show that it is possible to obtain the total wave transition through a plane defect. We determine the condition for realizing of such a resonance. We obtain the reflection and transition coefficients in the vicinity of the resonance. We establish that complete wave propagation with nonzero defect parameters can occur only when the nonlinear properties of the defect are taken into account.

Mitigation of liquid sloshing in a rectangular tank due to slotted porous screen

2020 ◽  
Vol 234 (3) ◽  
pp. 686-698
Author(s):  
Sunny Kumar Poguluri ◽  
Il-Hyoung Cho
Keyword(s):  
Free Surface ◽  
Numerical Technique ◽  
Liquid Sloshing ◽  
Tank Wall ◽  
Air Entrapment ◽  
Jet Formation ◽  
Induced Motion ◽  
Free Surface Wave ◽  
Nonlinear Free Surface ◽  
Porous Screen

Liquid sloshing inside a tank with a slotted porous screen at the center is studied based on numerical and experimental methods. Slotted screens with three different porosities (0.0964, 0.1968 and 0.3022) for two submergence depths of 1 and 2 cm have been considered. One of the main advantages of the slotted screens is that the resonance frequency of the sloshing tank can be altered and the sloshing-induced motion/load can be suppressed by energy dissipation across the porous screen. The complexities of slotted screens equipped in a sloshing tank are accompanied by wave breaking, jet formation and liquid fragmentations which are commonly seen phenomena across the porous screen. These violent free surface behaviors in a tank are studied based on numerical simulations using the incompressible turbulent model and compared with the experiments. For the numerical sloshing tank with porous screen, free surface elevation and pressure at the tank wall are in good agreement with the experimental results. The adopted numerical technique will be able to capture the nonlinear free surface wave profile, air entrapment and jet formation across the screen in agreement with the experiments. For the fully submerged screen, the lowest resonance period shifted slightly to higher values. The sloshing tank equipped with porous screen of 0.1968 for the fully submerged screen predicted lower values of the amplification factor and pressure at the tank wall compared to other cases.

scholarly journals On sound waves of finite amplitude

1953 ◽  
Vol 216 (1127) ◽  
pp. 539-547 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Arbitrary Function ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Sound Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Integral ◽  
Gas Cloud

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = k ρ γ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.

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