The Inertial Pressure Concept for Determining the Wave Forces on Submerged Bodies

1982 ◽  
Vol 104 (1) ◽  
pp. 47-52
Author(s):  
T. E. Horton ◽  
M. J. Feifarek
Keyword(s):  
Three Dimensional ◽  
Offshore Structures ◽  
Empirical Approach ◽  
Wave Forces ◽  
Morison Equation ◽  
Sea State ◽  
Wave Kinematics ◽  
State Wave

A new concept is presented which is aimed at improving the methodology for determining the wave forces on offshore structures. The Inertial Pressure Concept (IPC) is based on a direct, empirical approach to calculating forces. The resulting method can be formulated to include realistic sea state wave kinematics while not being dependent on a particular kinematic representation. Futhermore, the method should be as easy to apply as the Morison equation, but will allow diffraction and three-dimensional aspects to be considered.

A Hybrid Integral Equation Method for Wave Forces on Three-Dimensional Offshore Structures

1987 ◽  
Vol 109 (3) ◽  
pp. 229-236 ◽  
Author(s):  
M. M. F. Yuen ◽  
F. P. Chau
Keyword(s):  
Integral Equation ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Offshore Structures ◽  
Equation Method ◽  
Wave Forces ◽  
Test Cases ◽  
Outer Domain ◽  
Hybrid Integral

Wave forces on arbitrary-shaped three-dimensional offshore structures are analyzed by the proposed hybrid integral equation method. Eigenfunction expansion is used to represent velocity potential in the outer domain, while a set of integral equations is developed for the inner domain encompassing the structure. A floating dock and a step cylinder are used as test cases showing the validity of the method.

The Effect of Uncertainty in Wave Force Coefficients for Offshore Structures

1985 ◽  
Vol 25 (05) ◽  
pp. 757-764
Author(s):  
Kenneth G. Nolte
Keyword(s):  
Wave Force ◽  
Offshore Structures ◽  
Design Criteria ◽  
Wave Forces ◽  
Offshore Structure ◽  
Morison Equation ◽  
Force Coefficients ◽  
Wave Parameters ◽  
Random Occurrence ◽  
Wave Heights

Abstract A probability distribution, which incorporates the random occurrence of wave heights and the uncertainty in the force coefficients of the Morison equation, was derived for the forces on offshore structures. The random occurrence of wave heights was assumed to be described by a Weibull distribution, and the uncertainty in the force coefficients was assumed to be represented by a normal distribution. Wave force was assumed to be proportional to wave height raised to a power. The assumed distributions and force relationship may not describe exactly the actual problem within a general framework, but the assumptions are believed to be applicable to the range of wave heights and conditions occurring for the selection of static design criteria for the forces on offshore structures. The applicability of the assumptions is enhanced because the primary results are expressed as ratios, which require only relative accuracy and not quantitative accuracy. Introduction The wave forces on an offshore structure are determined by a wave theory (e.g., Stokes or stream function) that relates the water kinematics (velocity and acceleration) to the wave parameters (height and period) and a theory that relates the resulting pressures on the structure to the predicted water kinematics (e.g., the Morison equation or refraction theory). Generally, the Morison equation, which incorporates two force coefficients - the drag and inertia coefficients - is used. The wave parameters experienced by a structure during a storm are random. Also, inferred values of the force coefficients from field measurements indicate a random scatter from wave to wave caused by the random nature of the processes involved and imperfect wave and hydrodynamic theories. Therefore, the prediction of wave forces and, ultimately, the selection of design criteria for offshore structures involve both the random nature of the wave parameters (e.g., height) and the uncertainty in the force coefficients. Procedures for selecting wave heights for design criteria have received considerable attention and are well established; however, the problem of considering the uncertainty in the force coefficients has received little attention. Currently, there is no rational procedure to account generally for coefficient uncertainty except to use arbitrary, and potentially unrealistic, guidelines, such as the mean value plus a multiple of the standard deviation. The purpose of this paper is to provide a rational framework for dealing with the uncertainty in force coefficients. This framework is statistical and incorporates into the force statistics the uncertainty of the force coefficients and the random occurrence of the wave parameters. Background The wave force, Q, on an offshore structure is generally determined by the Morison equation,Equation 1 QD and QI are defined as the drag and inertia forces, respectively, per unit length acting normal to a structural element; CD and CI are the drag and inertia coefficients (i.e., the force coefficients); v and v are the water velocity and acceleration normal to the element; d is the element diameter; and ?w is the mass density of water.

Quantification of Predicted Wave Forces From Distant Elevation Measurements

2019 ◽  
Author(s):  
Spencer T. Hallowell ◽  
Sanjay R. Arwade ◽  
Hannah Johlas ◽  
Pedro Lomonaco ◽  
Andrew Myers
Keyword(s):  
Breaking Waves ◽  
Offshore Structures ◽  
Irregular Waves ◽  
Wave Forces ◽  
Structural Members ◽  
Prediction Equations ◽  
Linear Dispersion ◽  
Force Prediction ◽  
Wave Kinematics ◽  
Wave Measurements

Abstract The vast spatial scale of offshore structures causes wave loading to be correlated amongst nearby structural members. Certain engineering activities including health monitoring, maintenance, and preliminary design of offshore structures requires the prediction of wave forces on said structural members. The high cost and low availability of environmental wave measurements requires the reconstruction of wave kinematics and force profiles to accurately capture the forcing history on offshore structures. A method for predicting wave forces on a cylinder from nearby wave elevation measurements is proposed. The formulation utilizes the Fast Fourier Transform to calculate wave kinematics propagation in the frequency domain and applies the kinematics to the Morison equation for calculation of cylinder forces. The prediction equations are applied to three types of waves: regular periodic waves, random irregular waves, and solitary breaking waves, and the error in both elevation prediction and force prediction when compared to measured values is calculated. The force prediction equations were shown to perform best for small wave heights, with errors as low as 5% in the force predictions for small regular and irregular waves. The error in force prediction increases nonlinearly with the increase in wave height due to the deficiencies of the linear dispersion relationship used in the formulation.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

Effect of Air Fraction on Force Coefficients in Oscillatory Flow

2021 ◽  
Author(s):  
Malene Hovgaard Vested ◽  
Erik Damgaard Christensen
Keyword(s):  
High Speed ◽  
Offshore Structures ◽  
Air Injection ◽  
Wave Loads ◽  
Morison Equation ◽  
Force Coefficients ◽  
Air Content ◽  
Set Up ◽  
High Level ◽  
Spilling Breakers

Abstract The forces on marine and offshore structures are often affected by spilling breakers. The spilling breaker is characterized by a roller of mixed air and water with a forward speed approximately equal to the wave celerity. This high speed in the top of the wave has the potential to induce high wave loads on upper parts of the structures. This study analyzed the effect of the air content on the forces. The analyses used the Morison equation to examine the effect of the percentage of air on the forces. An experimental set-up was developed to include the injection of air into an otherwise calm water body. The air-injection did introduce a high level a turbulence. It was possible to assess the amount of air content in the water for different amounts of air-injection. In the mixture of air and water the force on an oscillating square cylinder was measured for different levels of air-content, — also in the case without air. The measurements indicated that force coefficients for clear water could be use in the Morison equation as long as the density for water was replaced by the density for the mixture of air and water.

Detailed Study on Breaking Wave Interactions With a Jacket Structure Based on Experimental Investigations

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Jithin Jose ◽  
Olga Podrażka ◽  
Ove Tobias Gudmestad ◽  
Witold Cieślikiewicz
Keyword(s):  
Wind Turbines ◽  
Wave Breaking ◽  
Offshore Structures ◽  
Offshore Wind ◽  
Wave Forces ◽  
Breaking Wave ◽  
Offshore Wind Turbines ◽  
Wave Parameters ◽  
Wave Slamming ◽  
Breaking Wave Forces

Wave breaking is one of the major concerns for offshore structures installed in shallow waters. Impulsive breaking wave forces sometimes govern the design of such structures, particularly in areas with a sloping sea bottom. Most of the existing offshore wind turbines were installed in shallow water regions. Among fixed-type support structures for offshore wind turbines, jacket structures have become popular in recent times as the water depth for fixed offshore wind structures increases. However, there are many uncertainties in estimating breaking wave forces on a jacket structure, as only a limited number of past studies have estimated these forces. Present study is based on the WaveSlam experiment carried out in 2013, in which a jacket structure of 1:8 scale was tested for several breaking wave conditions. The total and local wave slamming forces are obtained from the experimental measured forces, using two different filtering methods. The total wave slamming forces are filtered from the measured forces using the empirical mode decomposition (EMD) method, and local slamming forces are obtained by the frequency response function (FRF) method. From these results, the peak slamming forces and slamming coefficients on the jacket members are estimated. The breaking wave forces are found to be dependent on various breaking wave parameters such as breaking wave height, wave period, wave front asymmetry, and wave-breaking positions. These wave parameters are estimated from the wave gauge measurements taken during the experiment. The dependency of the wave slamming forces on these estimated wave parameters is also investigated.

scholarly journals THE DYNAMIC RESPONSE OF OFFSHORE STRUCTURES TO TIME-DEPENDENT FORCES

1964 ◽  
Vol 1 (9) ◽  
pp. 29
Author(s):  
William S. Gaither ◽  
David P. Billington
Keyword(s):  
Degrees Of Freedom ◽  
Wind Waves ◽  
Offshore Structures ◽  
Time Dependent ◽  
Wave Forces ◽  
Ocean Bottom ◽  
Single Wave ◽  
Single Degree Of Freedom ◽  
The Many ◽  
Floating Objects

This paper is addressed to the problem of structural behavior in an offshore environment, and the application of a more rigorous analysis for time-dependent forces than is currently used. Design of pile supported structures subjected to wave forces has, in the past, been treated in two parts; (1) a static analysis based on the loading of a single wave, and (2) a dynamic analysis which sought to determine the resonant frequency by assuming that the structure could be approximated as a single-degree-of-freedom system. (Ref. 4 and 6) The behavior of these structures would be better understood if the dynamic nature of the loading and the many degrees of freedom of the system were included. A structure which is built in the open ocean is subjected to periodic forces due to wind, waves, floating objects, and due occasionally to machinery mounted on the structure. To resist motion, the structure relies on the stiffness of the elements from which it is built and the restraints of the ocean bottom into which the supporting legs are driven.

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