A More Efficient Form of the Method of Moments for Derivation of Morison’s Force Coefficients

2007 ◽  
Author(s):  
G. Najafian
Keyword(s):  
Method Of Moments ◽  
Particle Velocity ◽  
Field Experiments ◽  
Inertial Force ◽  
New Method ◽  
Total Force ◽  
Wave Load ◽  
Sampling Variability ◽  
Water Particle ◽  
Empirical Coefficients

Morison’s equation is the most widely used method of predicting wave forces on slim cylindrical members of offshore structures. The equation assumes that the total force of the fluid is made up of a drag force and an inertial force, where the drag component is due to water particle velocity and the inertial component is due to water particle acceleration. In practice, the force uses two empirical coefficients, which are usually referred to as the drag and inertia coefficients. The values of these empirical coefficients are determined from laboratory and/or field experiments. In a typical wave load investigation, the wave force together with corresponding water particle velocity and acceleration are measured. The measured data is then analysed to calculate constant values for drag and inertia coefficients. One of the methods used in derivation of these coefficients is the method of moments. However, the coefficients obtained from this method show considerable scatter due to large sampling variability. The purpose of this paper is to introduce a more efficient form of the method of moments, which will lead to more accurate estimates of Morison’s coefficients by reducing their sampling variability. Simulated data has been used to compare the new method of moments with the conventional one. The results indicate that the new method is superior to the conventional one. This is particularly the case for drag-dominated forces.

Derivation of Morison’s Force Coefficients by Three Alternative Forms of the Method of Moments

2016 ◽  
Author(s):  
N. I. Mohd Zaki ◽  
M. K. Abu Husain ◽  
G. Najafian
Keyword(s):  
Conventional Method ◽  
Method Of Moments ◽  
Particle Velocity ◽  
Field Experiments ◽  
Inertial Force ◽  
Wave Force ◽  
Wave Load ◽  
Sampling Variability ◽  
Water Particle ◽  
Empirical Coefficients

Morison’s equation is the most widely used method of predicting wave forces on slim cylindrical members of offshore structures. The equation assumes that the wave force is composed of two components: a drag force and an inertial force, where the drag component is due to water particle velocity and the inertial component is due to water particle acceleration. Morison’s equation has two empirical coefficients, which are usually referred to as the drag and inertia coefficients. The values of these empirical coefficients are determined from laboratory and/or field experiments. In a typical wave load investigation, the wave force together with corresponding water particle velocity and acceleration are measured. The measured data is then analysed to calculate constant values for drag and inertia coefficients. One of the methods used in derivation of these coefficients is the (conventional) method of moments. However, the coefficients obtained from this method show considerable scatter due to large sampling variability. The purpose of this paper is to compare the sampling variability of drag and inertia coefficients from the conventional method of moments with those derived from two alternative forms of the method, i.e. methods of linear and low-order moments. Simulated data has been used to compare the efficiency of the three methods of moments. The results indicate that in most cases, the method of linear moments is superior to the other two methods. This is particularly true for drag-dominated forces.

scholarly journals The Effects on Water Particle Velocity of Wave Peaks Induced by Nonlinearity under Different Time Scales

2021 ◽  
Vol 9 (7) ◽  
pp. 748
Author(s):  
Aifeng Tao ◽  
Shuya Xie ◽  
Di Wu ◽  
Jun Fan ◽  
Yini Yang
Keyword(s):  
Particle Velocity ◽  
Modulation Instability ◽  
Wave Train ◽  
Quadratic Function ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Load ◽  
Freak Waves ◽  
Water Particle ◽  
Generation Mechanisms

The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters.

Technical note: A new method for the evaluation of puff dispersion field experiments for the validation of time-resolved dispersion simulations

2019 ◽  
Vol 210 ◽  
pp. 171-176
Author(s):  
Thorsten Wittemeier ◽  
Timothy G. Foat ◽  
Steven Herring ◽  
John S. Shrimpton ◽  
Zheng-Tong Xie
Keyword(s):  
Field Experiments ◽  
Technical Note ◽  
New Method ◽  
Time Resolved

scholarly journals DEVELOPMENT OF WAVE POWER GENERATION SYSTEM SUITABLE FOR INNER BAY

2020 ◽  
pp. 39
Author(s):  
Rioko Hirota ◽  
Takaaki Shigematsu ◽  
Kenji Katoh ◽  
Tatsuro Wakimoto ◽  
Shinya Yoshioka
Keyword(s):  
Power Generation ◽  
Particle Velocity ◽  
High Energy ◽  
Wave Power ◽  
Generation System ◽  
Water Particle ◽  
Water Turbine ◽  
Power Generation System ◽  
The Relationship ◽  
Wave Power Generation

With the increasing demand for renewable energy in the world, research contributing to the improvement of the technology level of wave power generation is essential. The authors have been developed a wave power generation system using port facilities in inner bays with high energy-consuming cities. In this study, the relationship between the rotational characteristics of a Savonius water turbine and the water particle velocity was quantitatively evaluated under the calm conditions of the inner bay, such as wave motion, flow, and coexistence of wave and current. According to the experimental results, it is found that the relationship between the rotational circumferential speed and the water particle velocity of the water turbine installed in a wave field tends to be different from that in a flow field and is evaluated by different equations. In addition, the relationship between circumferential velocity and the water particle velocity has also been formulated when installed in a wave-current coexistence field.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/KX0XBFuao48

scholarly journals KINEMATICS OF BREAKING WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 25 ◽  
Author(s):  
Edward B. Thornton ◽  
James J. Galvin ◽  
Frank L. Bub ◽  
David P. Richardson
Keyword(s):  
Solitary Waves ◽  
Particle Velocity ◽  
Asymptotic Expression ◽  
Breaking Waves ◽  
The Body ◽  
Time Dependent ◽  
Wave Crest ◽  
Periodic Waves ◽  
Water Particle ◽  
Highly Nonlinear

The sight and sound of breaking waves and surf is so familiar and enjoyable that we tend to forget how little we really understand about them. Why is it, that compared to other branches of wave studies our knowledge of breaking waves is so empirical and inexact? The reason must lie partly in the difficulty of finding a precise mathematical description of a fluid flow that is in general nonlinear and time-dependent. The fluid accelerations can no longer be assumed t o be small compared t o gravity, as in Stokes's theory for periodic waves and the theory of cnoidal waves in shallow water, nor is the particle velocity any longer small compared to the phase velocity. The aim of this paper is to bring together s ome recent contributions to the calculation both of steep symmetric waves and of time-dependent surface waves. These have a bearing on the behaviour of whitecaps in deep water and of surf in the breaker zone . Since spilling breakers in gently shoaling water closely resemble solitary waves, we begin with the description of solitary waves of limiting amplitude, then discuss steep waves of arbitrary height. The observed intermittency of whitecaps is discussed in terms of the energy maximum, as a function of wave steepness, In Sections 6 and 7 a simpler description of steady symmetric waves is proposed, using an asymptotic expression for the flow near the wave crest. Finally we describe a new numerical technique (MEL, or mixed Eulerian-Lagrangian) with which it has been found possible to follow the development of periodic waves past the point when overturning takes place. Measurement of waves, and vertical and horizontal water particle velocities were made of spilling, plunging and surging breakers at sandy beaches in the vicinity of Monterey, California. The measured breaking waves, derived characteristically from swell-type waves, can be described as highly nonlinear. Spectra and cross spectra were calculated between waves and velocities. Secondary waves were noted visually and by the strong harmonics in the spectra. The strength of the harmonics is related to the beach steepness, wave height and period. The phase difference between waves and horizontal velocities indicates the unstable crest of the wave leads the velocities on the average by 5-20 degrees. Phase measurements between wave gauges in a line perpendicular to the shore show breaking waves to be frequency nondispersive indicating phase-coupling of the various wave components. The coherence squared values between the sea surface elevation and the horizontal water particle velocity were high in all runs, ranging above 0.8 at the peak of the spectra. The high coherence suggests that most of the motion in the body of breaking waves is wave-induced and not turbulent.

scholarly journals A NEW METHOD OF PERFORMING FIELD TRIALS

1969 ◽  
Vol 28 (1) ◽  
pp. 22-34
Author(s):  
Bernardo G. Capó
Keyword(s):  
Field Experiments ◽  
Field Tests ◽  
Field Trials ◽  
New Method ◽  
Numerical Example ◽  
Fertilizer Experiment ◽  
Treatment Experiment

A new method of performing field experiments with relatively small numbers of treatments is described. The requirement to be fulfilled by the layouts of such field tests is specified and examples of possible designs for a 5-treatment experiment are illustrated. The theory of the procedure of calculation is discussed and a numerical example of said calculations is furnished in connection with the interpretation of a fertilizer experiment performed with cotton.

Field Observation of the Wave-Induced Water Particle Velocity in the Surf Zone

1980 ◽  
Vol 23 (1) ◽  
pp. 81-89 ◽  
Author(s):  
Masaru Mizuguchi ◽  
Masahiko Isobe ◽  
Shintaro Hotta ◽  
Kiyoshi Horikawa
Keyword(s):  
Particle Velocity ◽  
Field Observation ◽  
Surf Zone ◽  
Water Particle ◽  
Wave Induced

scholarly journals VORTEX FORMATION IN PLUNGING BREAKER

1986 ◽  
Vol 1 (20) ◽  
pp. 54 ◽  
Author(s):  
T. Sakai ◽  
T. Mizutani ◽  
H. Tanaka ◽  
Y. Tada
Keyword(s):  
Flow Visualization ◽  
Particle Velocity ◽  
Vortex Formation ◽  
Water Particle ◽  
Mac Method ◽  
Long Wave ◽  
Wave Celerity ◽  
Maximum Water ◽  
Slope Beach ◽  
Plunging Breaker

By a flow visualization of a plunging breaker on 1/20 slope beach in a wave tank, an existence of 2nd and 3rd horizontal vortices(Miller, 1976) and slanting vortex (Nadaoka et al., 1986) is confirmed. A MAC method is applied to simulate a violent motion after an impinging of a jet from a crest of a plunging breaker on the trough surface. The calculated maximum water particle velocity in the jet is found to reach three times the linear long wave celerity. Values of circulation of the first four horizontal vortices are calculated and their changes in time are discussed.

Poisson convergence and semi-induced properties of random graphs

1987 ◽  
Vol 101 (2) ◽  
pp. 291-300 ◽  
Author(s):  
Michał Karoński ◽  
Andrzej Ruciński
Keyword(s):  
Asymptotic Distribution ◽  
Random Graph ◽  
Random Graphs ◽  
Method Of Moments ◽  
Traditional Method ◽  
General Setting ◽  
Asymptotic Distributions ◽  
New Method ◽  
Isolated Trees ◽  
Ingenious Method

Barbour [l] invented an ingenious method of establishing the asymptotic distribution of the number X of specified subgraphs of a random graph. The novelty of his method relies on using the first two moments of X only, despite the traditional method of moments that involves all moments of X (compare [8, 10, 11, 14]). He also adjusted that new method for counting isolated trees of a given size in a random graph. (For further applications of Barbour's method see [4] and [10].) The main goal of this paper is to show how this method can be extended to a general setting that enables us to derive asymptotic distributions of subsets of vertices of a random graph with various properties.

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