TIME-DOMAIN SIMULATION OF THE GENERATION AND PROPAGATION OF SECOND-ORDER STOKES WAVES IN A TWO-DIMENSIONAL WAVE FLUME. PART I: MONOCHROMATIC WAVEMAKER MOTIONS

The effect of gradation of armour stones and the amount of rounded stones in the armour on dynamically stable breakwaters was assessed in a two-dimensional wave flume. A total of 52 series of tests were undertaken at the Coastal Engineering Research Laboratory of Queen's University, Kingston, Canada using irregular waves. Profiles of the structure during the various stages of reshaping were measured using a semiautomatic profiler developed for this study. Four gradations of armour stones were used, giving a range in uniformity coefficient of 1.35–5.4. The volume of stones and the initial berm width required for the development of a stable profile, along with the extent to which the toe of the structure progressed seaward, were chosen as representative parameters of the reshaped breakwater. The results indicated that the toe width formed as a result of reshaping and the area of stones required for reshaping were dependent on the gradation of the armour stones. The initial berm width required for reshaping was also found to be dependent on the gradation and the percentage of rounded stones in the armour. Key words: breakwaters, dynamic stability, hydraulic models, stability, armour stones.

Download Full-text

Non-Gaussian Random Wave Simulation by Two-Dimensional Fourier Transform and Linear Oscillator Response to Morison Force

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2783888 ◽

2007 ◽

Vol 129 (4) ◽

pp. 327-334 ◽

Cited By ~ 6

Author(s):

Xiang Yuan Zheng ◽

Torgeir Moan ◽

Ser Tong Quek

Keyword(s):

Fourier Transform ◽

Time Domain ◽

Two Dimensions ◽

Second Order ◽

Linear Oscillator ◽

Interaction Matrix ◽

Random Wave ◽

Two Dimensional ◽

Near Surface ◽

Non Gaussian

The one-dimensional fast Fourier transform (FFT) has been applied extensively to simulate Gaussian random wave elevations and water particle kinematics. The actual sea elevations/kinematics exhibit non-Gaussian characteristics that can be represented mathematically by a second-order random wave theory. The elevations/kinematics formulations contain frequency sum and difference terms that usually lead to expensive time-domain dynamic analyses of offshore structural responses. 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 forward FFT are implemented, respectively, across the two dimensions of the wave interaction matrix. Given specified wave conditions, the statistics of simulated elevations/kinematics compare well with not only the empirical fits but also the analytical solutions based on a modified eigenvalue/eigenvector approach, while the computational effort of simulation is very economical. In addition, the stochastic analyses in both time domain and frequency domain show that, attributable to the second-order nonlinear wave effects, the near-surface Morison force and induced linear oscillator response are more non-Gaussian than those subjected to Gaussian random waves.

Download Full-text

Lacunas in two-dimensional wave propagation

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100041803 ◽

1967 ◽

Vol 63 (3) ◽

pp. 819-825 ◽

Cited By ~ 36

Author(s):

R. Burridge

Keyword(s):

Wave Propagation ◽

Second Order ◽

Sufficient Condition ◽

Two Dimensional ◽

Two Space Dimensions ◽

Simple Sufficient Condition ◽

General Work ◽

Dimensional Wave

AbstractA simple sufficient condition is given for the existence of a lacuna in two-dimensional wave propagation governed by an equation of the second order. This work was inspired by Petrowsky's very general work (Petrowsky (3)) but for waves in two space dimensions we do not need the sophisticated machinery developed by him.

Download Full-text