Current responses of first and second order in a collisionless plasma. III. Three‐wave interaction in periodic plasmas

The one-dimensional Fast Fourier Transform (FFT) has been extensively applied to efficiently simulate Gaussian wave elevation and water particle kinematics. The actual sea elevation/kinematics exhibit non-Gaussianities that mathematically can be represented by the second-order random wave theory. The elevation/kinematics formulation contains double-summation frequency sum and difference terms which in computation make the dynamic analysis of offshore structural response prohibitive. This study aims at a direct and efficient two-dimensional FFT algorithm for simulating the frequency sum terms. For the frequency difference terms, inverse FFT and FFT are respectively implemented across the two dimensions of the wave interaction matrix. Given specified wave conditions, not only the wave elevation but kinematics and associated Morison force are simulated. Favorable agreements are achieved when the statistics of elevation/kinematics are compared with not only the empirical fits but the analytical solutions developed based on modified eigenvalue/eigenvector approach, while the computation effort is very limited. In addition, the stochastic analyses in both time-and frequency domains show that the near-surface Morison force and induced linear oscillator response exhibits stronger non-Gaussianities by involving the second-order wave effects.

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Ultrasonic wave interaction with a thin anisotropic layer between two anisotropic solids. II. Second‐order asymptotic boundary conditions

The Journal of the Acoustical Society of America ◽

10.1121/1.407194 ◽

1993 ◽

Vol 94 (6) ◽

pp. 3405-3420 ◽

Cited By ~ 45

Author(s):

S. I. Rokhlin ◽

W. Huang

Keyword(s):

Boundary Conditions ◽

Ultrasonic Wave ◽

Wave Interaction ◽

Second Order ◽

Anisotropic Layer ◽

Asymptotic Boundary

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Numerical calculation of the effective second-order nonlinear coefficient along collinear phase-matching directions inside nonlinear crystals in three-wave interaction

IEEE Journal of Quantum Electronics ◽

10.1109/3.481865 ◽

1996 ◽

Vol 32 (2) ◽

pp. 183-191 ◽

Cited By ~ 6

Author(s):

Jih-Fu Trevor Wang ◽

K. Daneshvar

Keyword(s):

Numerical Calculation ◽

Nonlinear Coefficient ◽

Wave Interaction ◽

Second Order ◽

Phase Matching ◽

Nonlinear Crystals

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Non-Linear Wave Diffraction Around a Moored Ship

23rd International Conference on Offshore Mechanics and Arctic Engineering, Volume 1, Parts A and B ◽

10.1115/omae2004-51589 ◽

2004 ◽

Author(s):

J. Zang ◽

R. Gibson ◽

P. H. Taylor ◽

R. Eatock Taylor ◽

C. Swan

Keyword(s):

Wave Diffraction ◽

Scattering Problem ◽

Wave Interaction ◽

Wave Structure ◽

Second Order ◽

Linear Wave ◽

Wave Impact ◽

Non Linear ◽

Focused Wave ◽

Run Up

The objective of this research, part of the FP5 REBASDO Programme, is to examine the effects of directional wave spreading on the nonlinear hydrodynamic loads and the wave run-up around the bow of a floating vessel (FPSO) in random seas. In this work, the non-linear wave scattering problem is solved by employing a quadratic boundary element method. An existing scheme (DIFFRACT developed in Oxford) has been extended to deal with uni-directional and directional bi-chromatic input wave systems, calculating second-order wave diffraction under regular waves and focused wave groups. The second order wave interaction with a floating vessel in a unidirectional focused wave group is presented in this paper. Comparison of numerical results and the experimental measurements conducted at Imperial College shows excellent agreement. The second-order free surface components at the bow of the ship are very significant, and cannot be neglected if one requires accurate prediction of the wave-structure interaction; otherwise a major underestimation of the wave impact on the structure could occur.

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