scholarly journals WAVE SCATTERING BY PERMEABLE AND IMPERMEABLE BREAKWATER OF ARBITRARY SHAPE

1974 ◽  
Vol 1 (14) ◽  
pp. 110
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Yasu Yumura
Keyword(s):  
Arbitrary Shape ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Floating Body ◽  
Wave Forces ◽  
Method Of Calculation ◽  
Wave Channel ◽  
Method Of Solution ◽  
Special Case

This paper deals with a theoretical method of calculation of the fluid motion, when a sinusoidal plane wave incidents to a permeable breakwater of arbitrary shape at constant water depth and shows that the problem for impermeable breakwater is solved as a special case of this method. The method described here is the extension of the author's method of solution for two-dimensional permeable breakwater by the method of continuation of velocity potentials for two different fluid regions into three-dimensional problems by means of Green functions. Here, the analytical process of calculation is presented and as representative examples, wave height distributions and wave forces around an isolated elliptic- and rectangular breakwater are calculated and compared with experiments in wave channel. The principle of this method is also applied to the analysis of submerged and semi-immersed fixed cylinder and the motions of floating body of arbitrary.

scholarly journals WAVE FORCES ON SQUARE CAISSONS

1976 ◽  
Vol 1 (15) ◽  
pp. 132 ◽  
Author(s):  
G.R. Mogridge ◽  
W.W. Jamieson
Keyword(s):  
Experimental Data ◽  
Theoretical Method ◽  
Wave Forces ◽  
Simple Method ◽  
Method Of Calculation ◽  
Wave Flume ◽  
Wide Range ◽  
Wave Heights ◽  
And Storage ◽  
Water Depths

The forces and overturning moments exerted by waves on large vertical square-section caissons have been measured in the laboratory. Each model caisson extended from the bottom of a wave flume through the water surface and was oriented either with one side perpendicular to the direction of wave propagation or turned through an angle of forty-five degrees to this position. For a given orientation, each model was tested for a range of wave heights (up to the point of breaking) for various wave periods and water depths. A digital computer was used for the acquisition, processing, plotting and storage of the experimental data. In addition to the experimental work, an approximate theoretical method is presented which allows the wave loadings on a square caisson to be estimated by means of a simple desk calculation. The experimental data shows that this simple method of calculation is reasonably accurate over a wide range of wave conditions and caisson sizes.

A Nonlinear-PH Method of Solution for Journal Gas Bearings

1976 ◽  
Vol 98 (4) ◽  
pp. 613-619 ◽  
Author(s):  
M. J. Cohen
Keyword(s):  
Linear Form ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Small Perturbations ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution ◽  
In Series ◽  
Gas Bearing

This paper describes a method of solving the Reynolds equations governing the fluid motion in an infinite journal gas bearing. The method derives from an exact transformation of the classical equations to a quasi-linear form. The only assumption made is the isothermal one which in practice closely describes the changes in the state of the gas within the bearing. The solution to the transformed equation for ph is sought in series and there are no difficulties in taking more terms into considerations, apart from algebraic ones. A first order solution is immediately obtained and corresponds as an approximation to any of the following methods: small perturbations (Ausman [1]) Katto and Soda [2], linear-ph (Ausman [3]) Harrison [4]. A higher order solution is also presented which requires little more algebra for its derivation. The extension of the method to three-dimensional gas journal bearings is also outlined.

RAPID COMPUTATION OF GRAVITATIONAL ATTRACTION OF THREE‐DIMENSIONAL BODIES OF ARBITRARY SHAPE

Geophysics ◽  
1960 ◽  
Vol 25 (1) ◽  
pp. 203-225 ◽  
Author(s):  
Manik Talwani ◽  
Maurice Ewing
Keyword(s):  
Gravity Anomaly ◽  
Arbitrary Shape ◽  
High Speed ◽  
Three Dimensional ◽  
Isostatic Compensation ◽  
External Point ◽  
Spherical Earth ◽  
Terrain Corrections ◽  
High Degree ◽  
Special Case

An expression is derived for the gravity anomaly at an external point caused by a horizontal lamina with the boundary of an irregular polygon. This expression is put in a form suitable for computation by a high speed digital computer. By making the number of sides of the polygon sufficiently large, any irregular outline can be closely approximated. Any three dimensional body can be represented by contours. By replacing each contour by a polygonal lamina, the anomaly caused by it can be obtained at any external point. By a system of interpolation between contours combined with a numerical integration the gravity anomaly caused by the three‐dimensional body can be calculated to a high degree of precision. This method may also be used for rapidly computing terrain corrections on a flat earth. By making a small modification it can further be adopted for computing the terrain correction as well as local isostatic compensation on the Airy system up to the external radius of Hayford zone O on a spherical earth. The expression for the anomaly caused by a horizontal polygonal lamina is also obtained for the special case when the sides of the polygon are alternately parallel to the x- and y-axes, that is, the polygonal lamina can be divided into a number of rectangular laminae. A chart is provided for the hand computation of the gravity anomaly in this case.

scholarly journals A Variance Gamma model for Rugby Union matches

2020 ◽  
Vol 17 (1) ◽  
pp. 67-75
Author(s):  
John Fry ◽  
Oliver Smart ◽  
Jean-Philippe Serbera ◽  
Bernhard Klar
Keyword(s):  
Three Dimensional ◽  
Rugby Union ◽  
Three Dimensional Model ◽  
Gamma Model ◽  
Variance Gamma ◽  
Poisson Models ◽  
History Of ◽  
Bonus Points ◽  
Variance Gamma Model ◽  
Special Case

Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

Secondary motion in convection layers generated by lateral heating of a solute gradient

2002 ◽  
Vol 455 ◽  
pp. 1-19 ◽  
Author(s):  
CHO LIK CHAN ◽  
WEN-YAU CHEN ◽  
C. F. CHEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Convection Cell ◽  
Experimental Conditions ◽  
Longitudinal Plane ◽  
Secondary Motion ◽  
Solute Gradient

The three-dimensional motion observed by Chen & Chen (1997) in the convection cells generated by sideways heating of a solute gradient is further examined by experiments and linear stability analysis. In the experiments, we obtained visualizations and PIV measurements of the velocity of the fluid motion in the longitudinal plane perpendicular to the imposed temperature gradient. The flow consists of a horizontal row of counter-rotating vortices within each convection cell. The magnitude of this secondary motion is approximately one-half that of the primary convection cell. Results of a linear stability analysis of a parallel double-diffusive flow model of the actual ow show that the instability is in the salt-finger mode under the experimental conditions. The perturbation streamlines in the longitudinal plane at onset consist of a horizontal row of counter-rotating vortices similar to those observed in the experiments.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

Numerical Research on FPSOs With Green Water Occurrence

2009 ◽  
Vol 53 (01) ◽  
pp. 7-18
Author(s):  
Renchuan Zhu ◽  
Guoping Miao ◽  
Zhaowei Lin
Keyword(s):  
Three Dimensional ◽  
Green Water ◽  
Floating Body ◽  
Incoming Wave ◽  
Model Case ◽  
Floating Structures ◽  
Design And Optimization ◽  
Head Waves ◽  
Wave Heights ◽  
The Impact

Green water loads on sailing ships or floating structures occur when an incoming wave significantly exceeds freeboard and water runs onto the deck. In this paper, numerical programs developed based on the platform of the commercial software Fluent were used to numerically model green water occurrence on floating structures exposed to waves. The phenomena of the fixed floating production, storage, and offloading unit (FPSO) model and oscillating vessels in head waves have been simulated and analyzed. For the oscillating floating body case, a combination idea is presented in which the motions of the FPSO are calculated by the potential theory in advance and computional fluid dynamics (CFD) tools are used to investigate the details of green water. A technique of dynamic mesh is introduced in a numerical wave tank to simulate the green water occurrence on the oscillating vessels in waves. Numerical results agree well with the corresponding experimental results regarding the wave heights on deck and green water impact loads; the two-dimensional fixed FPSO model case conducted by Greco (2001), and the three-dimensional oscillating vessel cases by Buchner (2002), respectively. The research presented here indicates that the present numerical scheme and method can be used to actually simulate the phenomenon of green water on deck, and to predict and analyze the impact forces on floating structures due to green water. This can be of great significance in further guiding ship design and optimization, especially in the strength design of ship bows.

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