The Diffraction of Multidirectional Random Waves by Trapezoidal Submarine Pits

2003 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams ◽  
Sung Duk Kim
Keyword(s):  
Numerical Model ◽  
Wave Diffraction ◽  
Boundary Integral ◽  
Random Wave ◽  
Linear Wave ◽  
Wave System ◽  
Random Waves ◽  
Random Surface ◽  
Directional Spectrum ◽  
Integral Equation Approach

A numerical model is presented to predict the interaction of multidirectional random surface waves with one or more trapezoidal submarine pits. In the present formulation, each pit may have a different side slope, while the four side slopes at the interior edge of any given pit are assumed equal. The water depth in the fluid region exterior to the pits is taken to be uniform, and the solution method for a random wave system involves the superposition of linear-wave diffraction solutions based on a two-dimensional boundary integral equation approach. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The results of the present numerical model have been compared with those of previous theoretical studies for regular and random wave diffraction by single or multiple rectangular pits. Reasonable agreement was obtained in all cases. Based on these comparisons it is concluded that the present numerical model is an accurate and efficient tool to predict the wave field around multiple submarine pits of trapezoidal section in many practical situations.

A Three-Dimensional Modeling of Multidirectional Random Wave Interactions by Multiple Rectangular Submarine Pits

2004 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams ◽  
Sung Duk Kim
Keyword(s):  
Numerical Model ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Approach ◽  
Random Wave ◽  
Random Surface ◽  
Directional Spectrum ◽  
Practical Applications ◽  
Three Dimensional Modeling

A three-dimensional numerical model is presented to predict the interactions of multidirectional random surface waves with one or more rectangular submarine pits. The water depth in the fluid region exterior to the pits is taken to be uniform. The three-dimensional Green function in the boundary integral equation, obtained by Green’s second identity, has been used for the solution of the velocity potential and its derivative in fluid interface between regions, and also a form of the Fourier expansion is utilized for the solution of the velocity potential in the interior region. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The present method is based on the cumulative superposition of linear diffraction solutions obtained by a three-dimensional boundary integral approach. The results of the present model have been compared with those of previous theoretical studies for both regular and random wave diffraction by single or multiple pits. Reasonable agreement was consistently obtained in all cases. In accordance with good agreement from these comparisons, it is concluded that the present numerical model may accurately be utilized to predict the three-dimensional wave field around multiple submarine pits or navigation channels in many practical applications.

The Diffraction of Multidirectional Random Waves by Rectangular Submarine Pits

2004 ◽  
Vol 126 (1) ◽  
pp. 9-15 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams
Keyword(s):  
Water Wave ◽  
Wave Theory ◽  
Boundary Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Random Waves ◽  
Discrete Form ◽  
Random Surface ◽  
Directional Spectrum ◽  
Dimensional Boundary

The diffraction of multidirectional random surface waves with one or more rectangular submarine pits is investigated theoretically. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The numerical model involves the superposition of regular-wave diffraction solutions based on linearized shallow water wave theory obtained by a two-dimensional boundary integral approach for water of uniform depth. Numerical results are presented for multi-directional random waves that illustrate the effect of the various wave and pit parameters on the diffraction characteristics of typical single and multiple pit systems.

The Diffraction of Multidirectional Random Waves by Rectangular Submarine Pits

2002 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams
Keyword(s):  
Boundary Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Regular Wave ◽  
Random Waves ◽  
Shallow Water Theory ◽  
Discrete Form ◽  
Random Surface ◽  
Directional Spectrum ◽  
Dimensional Boundary

The diffraction of multidirectional random surface waves with one or more rectangular submarine pits is investigated theoretically. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The numerical model involves the superposition of regular-wave diffraction solutions based on linearized shallow water theory obtained by a two-dimensional boundary integral approach for water of uniform depth. Numerical results are presented for multi-directional random waves that illustrate the effect of the various wave and pit parameters on the diffraction characteristics of typical single and multiple pit systems.

scholarly journals DIFFRACTION DIAGRAMS FOR DIRECTIONAL RANDOM WAVES

1978 ◽  
Vol 1 (16) ◽  
pp. 35 ◽  
Author(s):  
Yoshimi Goda ◽  
Tomotsuka Takayama ◽  
Tasumasa Suzuki
Keyword(s):  
Wave Diffraction ◽  
Spectral Characteristics ◽  
Wave Spectrum ◽  
Standard Form ◽  
Random Wave ◽  
Random Waves ◽  
Directional Spectrum ◽  
Spreading Function ◽  
Wave Heights ◽  
Directional Wave

Conventional wave diffraction diagrams often yield erroneous estimation of wave heights behind breakwaters in the sea, because they are prepared for monochromatic waves while actual waves in the sea are random with directional spectral characteristics. A proposal is made for the standard form of directional wave spectrum on the basis of Mitsuyasu's formula for directional spreading function. A new set of diffraction diagrams have been constructed for random waves with the proposed directional spectrum. Problems of multi-diffraction and multi-reflection within a harbour can also be solved with serial applications of random wave diffraction.

scholarly journals Comparison of Extreme Surface Elevation for Linear and Nonlinear Random Wave Theory for Offshore Structures

2018 ◽  
Vol 203 ◽  
pp. 01021
Author(s):  
Nurul 'Azizah Mukhlas ◽  
Noor Irza Mohd Zaki ◽  
Mohd Khairi Abu Husain ◽  
Gholamhossein Najafian
Keyword(s):  
Probabilistic Approach ◽  
Wave Theory ◽  
Offshore Structures ◽  
Random Wave ◽  
Linear Wave ◽  
Random Waves ◽  
Sea State ◽  
Higher Order Terms ◽  
Structural Responses ◽  
Nonlinear Random Wave

For offshore structural design, the load due to wind-generated random waves is usually the most important source of loading. While these structures can be designed by exposing them to extreme regular waves (100-year design wave), it is much more satisfactory to use a probabilistic approach to account for the inherent randomness of the wave loading. This method allows the statistical properties of the loads and structural responses to be determined, which is essential for the risk-based assessment of these structures. It has been recognized that the simplest wave generation is by using linear random wave theory. However, there is some limitation on its application as some of the nonlinearities cannot be explained when higher order terms are excluded and lead to underestimating of 100-year wave height. In this paper, the contribution of nonlinearities based on the second order wave theory was considered and being tested at a variety of sea state condition from low, moderate to high. Hence, it was proven that the contribution of nonlinearities gives significant impact the prediction of 100-year wave's design as it provides a higher prediction compared to linear wave theory.

The effects of randomness on the stability of two-dimensional surface wavetrains

1978 ◽  
Vol 363 (1715) ◽  
pp. 525-546 ◽  
Keyword(s):  
Water Waves ◽  
Modulational Instability ◽  
Wave Spectrum ◽  
Random Wave ◽  
Length Scale ◽  
Wave System ◽  
Random Surface ◽  
Homogeneous Wave ◽  
Amplification Rate ◽  
The Stability

A simplified nonlinear spectral transport equation, for narrowband Gaussian random surface wavetrains, slowly varying in space and time, is derived fron the weakly nonlinear equations of Davey & Stewartson. The stability of an initially homogeneous wave spectrum, to small oblique wave perturbations is studied for a range of spectral bandwidths, resulting in an integral equation for the amplification rate of the disturbance. It is shown for random deep water waves that instability of the wavetrain can exist, as in the corresponding deterministic Benjamin-Feir (B-F) problem, provided that the normalized spectral bandwidth σ / k 0 is less than twice the root mean square wave slope, multiplied by a function of the perturbation wave angle ϕ = arctan ( m/l ). A further condition for instability is that the angle ϕ be less than 35.26°. It is demonstrated that the amplification rate, associated with the B-F type instability, diminishes and then vanishes as the correlation length scale of the random wave field ( ca . 1/ σ )is reduced to the order of the characteristic length scale for modulational instability of the wave system.

Modelling of Periodic and Random Wave Forces on Submarine Pipelines

2006 ◽  
Author(s):  
Francesco Aristodemo ◽  
Giuseppe R. Tomasicchio ◽  
Paolo Veltri
Keyword(s):  
Numerical Model ◽  
Laboratory Investigation ◽  
Time History ◽  
Hydrodynamic Forces ◽  
Random Wave ◽  
Wave Forces ◽  
Random Waves ◽  
Large Wave ◽  
Wave Flume ◽  
History Of

A numerical model for the prediction of the time variation of the flow field and the hydrodynamic forces on bottom submarine pipelines is proposed. The model is an extension for periodic and random waves of the Wake II hydrodynamic forces model (Soedigdo et al., 1999), originally proposed for sinusoidal waves. An extensive laboratory investigation has been carried out in order to calibrate the model. The numerical model is based on an analysis of the time history of the velocity field at each wave semi-cycle. A modified relationship of the wake velocity is introduced and the time history of the drag and lift hydrodynamic coefficients are obtained using a Gauss integration of the start-up function. The laboratory investigation was performed at the large wave flume of the Centro Sperimentale per Modelli Idraulici at Voltabarozzo (Padua, Italy). The tests were carried out by measuring the pressure values at 8 transducers mounted on a cylinder subjected to different periodic and random waves. The experiments refer to the range 4 ÷ 12 of the Keulegan-Carpenter number for periodic waves and to the range 4 ÷ 9 for random waves. The empirical parameters involved in the extended Wake II and in the classical Morison models were calibrated using the results of the sampled velocities and force time histories under different wave conditions. The comparisons between the experimental and numerical results indicate that the extended Wake II model allows an accurate evaluation of the peaks and of the phase shifts of the horizontal and vertical forces and is more accurate than the Morison model.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

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