Contributions to Second Order Directional Sea Simulation and Wave Forces

2007 ◽  
Author(s):  
Jagat N. Sharma ◽  
Robert G. Dean
Keyword(s):  
Pile Group ◽  
Simulation Method ◽  
Wave Force ◽  
Offshore Structures ◽  
Reduction Factor ◽  
Second Order ◽  
Order Effects ◽  
Wave Forces ◽  
Single Pile ◽  
Wave Methods

We briefly describe a method for simulating second order directional seas and associated wave forces. We present wave force calculations for simplified forms of real offshore structures. Compared to unidirectional wave force calculations, this method reduces total design wave force. Complex subharmonic motion of large floating structures can be easily understood within the framework of this simulation method. A real sea is first represented by discrete linear waves of many frequencies traveling in many directions. Then, second order effects are calculated using equations derived for this purpose. The sum of linear and nonlinear waves is used to calculate wave forces on example offshore structures. The simulation method has been applied to calculate total wave forces on a single pile and a 4-pile group. Simulation method calculated wave forces on a single pile and a 4-pile group on a 60 ft square array are only 61% of wave forces using unidirectional wave methods. These results are the same as those obtained by a so-called hybrid method (Dean 1977) for the drag dominant case. When the pile separation is increased to 300 ft (similar to a TLP or a semisubmersible) the corresponding reduction factor varies from 0.79 for a unidirectional random sea to 0.61 for an omnidirectional random sea. Large offshore structures are relatively insensitive to the linear frequencies but could have very large response to the subharmonic frequencies in the simulation method. This is consistent with the field and laboratory observations.

Second-Order Diffraction Loads on Plural Vertical Cylinder With Arbitrary Cross Sections

1987 ◽  
Vol 109 (4) ◽  
pp. 314-319
Author(s):  
K. Masuda ◽  
W. Kato ◽  
H. Ishizuka
Keyword(s):  
Boundary Value Problem ◽  
Cross Sections ◽  
Present Method ◽  
Boundary Value ◽  
Vertical Cylinder ◽  
Wave Force ◽  
Second Order ◽  
Wave Forces ◽  
Order Diffraction ◽  
Rectangular Cylinders

The purpose of the present study is development of a powerful numerical method for calculating second-order diffraction loads on plural vertical cylinder with arbitrary cross sections. According to the present method, second-order wave force can be obtained from a linear radiation potential without solving second-order boundary value problem. The boundary value problem for the radiation potential is solved with the hybrid boundary element method. The computations for circular and rectangular cylinders were carried out and compared with the experiments. In addition, second-order wave forces on twin circular cylinder are calculated with the present method.

Effect of Seabed Slope on Offshore Pile Lateral Behaviour Under Wave Force

2010 ◽  
Author(s):  
Sathyanarayanan Dhandapani ◽  
Muthukkumaran Kasinathan
Keyword(s):  
Finite Element ◽  
Vertical Direction ◽  
Pile Group ◽  
Element Model ◽  
Wave Force ◽  
Wave Forces ◽  
Extreme Conditions ◽  
Offshore Platforms ◽  
Wave Loads ◽  
Offshore Structure

Fixed offshore platforms supported by pile foundations are required to resist dynamic lateral loading due to wave forces. The response of a jacket offshore tower is affected by the flexibility and nonlinear behavior of the supporting piles. In this study, a typical fixed offshore platform is chosen, and dynamic wave analysis is performed on it. Analysis has been performed for normal environmental conditions and extreme conditions. For the foundation, the deflections and reactions at regular intervals along the vertical direction from the seabed have been found out from the dynamic analysis, and the results have been compared for normal and extreme conditions. The aim of this study is to investigate the effects of the combined lateral and vertical loads on pile group foundation of a fixed offshore structure and the effects of seabed slope on the pile responses. To provide a more accurate and effective design for offshore pile foundation systems under axial structural loads and lateral wave loads, a finite element model which is modelled in FLAC3D is employed herein to determine the soil structure interaction under similar loading conditions. Three dimensional modelling and the analyses are done using FLAC3D — a finite element package.

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.

Nonlinear wave forces on a circular cylinder

1989 ◽  
Vol 16 (2) ◽  
pp. 182-187 ◽  
Author(s):  
Michael Isaacson ◽  
Qi-Hua Zuo
Keyword(s):  
Circular Cylinder ◽  
Nonlinear Wave ◽  
Perturbation Methods ◽  
Wave Force ◽  
Offshore Structures ◽  
Wave Forces ◽  
Ocean Engineering ◽  
Time Stepping ◽  
Wave Effects ◽  
Accuracy And Stability

Nonlinear wave forces on a surface-piercing vertical circular cylinder are considered using a time-stepping method previously developed which is based on Green's theorem. Possible improvements in the efficiency, accuracy, and stability of the method are considered. Results based on this method are compared with those obtained previously using perturbation methods as well as with experimental results. It is found that the time-stepping method adopted here is quite reasonable. Wave force coefficients are given as functions of the governing parameters of the problem and the importance of nonlinear wave effects on the forces is assessed. Key words: hydrodynamics, ocean engineering, offshore structures, waves, wave forces.

Focused Plunging Breaking Waves Impact on Pile Group in Finite Water Depth

2021 ◽  
pp. 1-17
Author(s):  
Ting Cui ◽  
Arun Kamath ◽  
Weizhi Wang ◽  
Lihao Yuan ◽  
Duanfeng Han ◽  
...  
Keyword(s):  
Water Depth ◽  
Pile Group ◽  
Breaking Waves ◽  
Offshore Structures ◽  
Structural Safety ◽  
Wave Forces ◽  
Pile Groups ◽  
Navier Stokes Equation ◽  
Finite Water Depth ◽  
Numerical Wave

Abstract Accuracy estimation of wave loading on cylinders in a pile group under different impact scenarios is essential for both the structural safety and cost of coastal and offshore structures. Differing from the interaction of waves with a single cylinder, less attention has been paid to pile groups under different arrangements. Numerical simulations of interactions between plunging breaking waves and pile group in finite water depth are performed using the two-phase flow model in REEF3D, an open-source computational fluid dynamics program to investigate the wave loads and flow kinematics characteristics. The Reynolds-averaged Navier-Stokes equation with the two equation k − ω turbulence model is adopted to resolve the numerical wave tank. The model is validated by comparing the numerical wave forces and free surface elevation with measurements from experiments. The computational results show fairly good agreement with experimental data. Four cases are simulated with different relative distances, numbers of cylinders and arrangements. Results show that the wave forces on cylinders in the pile group are effected by the relative distance between cylinders. The staggered arrangement has a significant influence on the wave forces on the first and second cylinder. The interaction inside a pile group mostly happens between the neighboring cylinders.

Correction factors for nonlinear runup and wave forces on a large cylinder

1994 ◽  
Vol 21 (5) ◽  
pp. 762-769 ◽  
Author(s):  
Michael Isaacson ◽  
Kwok Fai Cheung
Keyword(s):  
Experimental Studies ◽  
Diffraction Theory ◽  
Wave Force ◽  
Offshore Structures ◽  
Wave Forces ◽  
Correction Factors ◽  
Wave Loads ◽  
Wave Runup ◽  
Ocean Engineering ◽  
Simplified Approach

A recently developed numerical method for second-order wave diffraction is summarized and is used to develop a simplified approach to predicting nonlinear runup and maximum wave loads for large coastal and offshore structures subjected to regular waves. The perturbation method on which the method is based is extended to provide correction factors for the runup and maximum loads. These correction factors apply directly to the predictions of linear diffraction theory, and are independent of the wave height. The correction factors for runup, maximum force and maximum overturning moment are provided for a range of geometric parameters relating to the case of a large circular cylinder extending from the seabed to the free surface. Nonlinear runup and load maxima calculated by the correction factors are compared with the results of previous experimental studies; in general, favourable agreement is obtained. An example application of the proposed procedure is provided, the importance of nonlinear effects in the evaluation of runup and wave loads is discussed, and the limitations of the results are indicated. Key words: coastal structures, diffraction, hydrodynamics, ocean engineering, offshore structures, wave runup, wave force, waves.

A Theoretical Study on the Second-Order Wave Forces for Two-Dimensional Bodies

1989 ◽  
Vol 111 (1) ◽  
pp. 37-42 ◽  
Author(s):  
G. P. Miao ◽  
Y. Z. Liu
Keyword(s):  
Nonlinear Wave ◽  
Incident Wave ◽  
Theoretical Study ◽  
Nonlinear Effects ◽  
Offshore Structures ◽  
Second Order ◽  
Wave Forces ◽  
Two Dimensional ◽  
Regular Waves ◽  
Steady Wave

Nonlinear wave forces on fixed or floating offshore structures have attracted much attention recently. This paper deals with the nonlinear effects of regular waves on fixed two-dimensional bodies up to second-order terms. The second-order diffraction potential is solved consistently and the second-order steady wave forces and the biharmonic wave forces with frequency corresponding to the double of the incident wave frequency are obtained.

Second-Order Directional Seas and Associated Wave Forces

1981 ◽  
Vol 21 (01) ◽  
pp. 129-140 ◽  
Author(s):  
J.N. Sharma ◽  
R.G. Dean
Keyword(s):  
Hybrid Method ◽  
Time Domain ◽  
Pile Group ◽  
Second Order ◽  
Wave Forces ◽  
Linear Superposition ◽  
Directional Characteristics ◽  
Water Particle Kinematics ◽  
The Time Domain ◽  
Principle Of Linear Superposition

Abstract Most methods for wave force computation incorporate either the nonlinearities of the ocean surface for a single fundamental component or the random and/or directional characteristics using superposition of linear wave components. One exception is the intuitive "hybrid" method, which combines elements of linear and nonlinear waves. This paper describes and applies a method correct to the second order in wave height for calculating waves and wave forces caused by a directional wave spectrum on an offshore structure.Starting with a prescribed linear spectrum of directional waves, a set of random phases is generated and the second-order spectrum computed with phases defined by all contributing pairs of first-order components. Thus, with one realization of the spectrum complete up to the second order, the wave profile and water particle kinematics can be profile and water particle kinematics can be simulated in the time domain. The wave forces also are computed in the time domain, taking full account of their nonlinear and directional properties. The resulting wave forces at any level vary in direction and magnitude. The total wave forces summed over all piling of a structure are less than those for a unidirectional train of waves with the same one-dimensional spectrum.Several examples are presented to illustrate reductions in maximum wave forces caused by the directional distribution of waves. We found that for a single piling the maximum force decreases by a factor ranging from 1.0 to 0.61 as the directional spread increases from unidirectional to uniformity over a half plane. For a four-pile group on a square array of 300-ft (91.4-m) spacing, the corresponding decrease in the factor is 1.0 to 0.51 for a Bretschneider spectrum with a peak period of approximately 12 seconds. The results of this complete model are compared with the more intuitive and approximate hybrid method and are found to agree quite well. Force spectra are presented and discussed for the inline and transverse directions. Introduction The nonlinearity, randomness, and directionality of a real sea preclude a simple but realistic determination of wave loading on a single- or multiple-pile group. Presently, there are two essentially different but complementary methods for computing wave loadings. One method represents nonlinearities of a single wave composed of a characteristic fundamental period and its higher harmonics. A number period and its higher harmonics. A number of such theories have been-developed. Dalrymple extended the stream function approach of Dean, to waves on a shear current. Some of these theories adequately account for the nonlinearities; however, they avoid the random and directional characteristics of the sea surface. The second method uses the principle of linear superposition of an infinite principle of linear superposition of an infinite number of waves with given frequencies, amplitudes, and directions of propagation but independent phases; the total energy is distributed over a phases; the total energy is distributed over a continuum of frequencies and directions. In this manner, a three-dimensional Gaussian sea can be represented fully. However, ignoring the nonlinearities makes the random Gaussian model unrealistic - especially for large waves. SPEJ P. 129

Higher Order Wave Loading on Fixed, Slender, Surface-Piercing, Rigid Cylinders

1991 ◽  
Vol 113 (1) ◽  
pp. 23-29
Author(s):  
K. Thiagarajan ◽  
R. E. Baddour
Keyword(s):  
Dynamic Pressure ◽  
Wave Theory ◽  
Offshore Structures ◽  
Second Order ◽  
Pressure Effects ◽  
Inertia Force ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Loading ◽  
Theoretical Evaluation

The use of Morison’s equation together with the linear wave theory is considered a first approximation to evaluate the inline wave forces on a surface-piercing cylinder. Significant second-order forces are expected to arise from the waterline and dynamic pressure effects, even when a wave is described by the linear theory. Experiments have been carried out at the MUN (Memorial University of Newfoundland) wave tank facility to identify these second-order forces for various wave frequencies and for various cylinder diameters. A strain gage force transducer has been used for this purpose. First and second-order force components have been identified using a Fast Fourier Transform. Theoretical evaluation of wave forces involved computing components from Morison’s equation using second-order Stokes theory. The waterline forces and convective acceleration forces which contribute toward the total second-order force have also been evaluated. First-order results are in acceptance with previously established data. Theoretical considerations for second order are satisfactory. Scatter in second-order experimental results were observed. Different approaches to the second-order inertia force are compared. It is expected that the inclusion of second-order forces will lead to a better representation of wave loading on offshore structures.

Steep Wave Forces on Large Offshore Structures

1983 ◽  
Vol 23 (01) ◽  
pp. 184-190
Author(s):  
Michael de St. Q. Isaacson
Keyword(s):  
Integral Equation ◽  
Shallow Water ◽  
Integral Equation Method ◽  
Offshore Structures ◽  
Second Order ◽  
Equation Method ◽  
Wave Forces ◽  
Time Stepping ◽  
Green’S Theorem ◽  
Typical Design

Abstract A new numerical method for calculating the interaction of steep (nonlinear)ocean waves with large coastal or offshore structures of arbitrary shape is described. The evolution of the flow, and in particular the loads on the structure and the runup around it, are obtained by a time-stepping procedure in which the flow at each time step is calculated by an integral equation method based on Green's theorem. A few comparisons are made with available solutions and results are presented for a typical design wave in shallow water. The method is capable of predicting forces caused by steep waves accurately and without prohibitive computer effort. Introduction The prediction of wave forces on large offshore structures on the basis of linear diffraction theory, which is formally valid for small-amplitude sinusoidal waves, is now an established part of offshore design procedure. Reviews of the approaches generally used have been given by Hogben etal.,1 Isaacson,2 and Sarpkaya and Isaacson.3 To account more realistically for the effect of large wave heights, research recently has been directed primarily toward developing a second approximation based on the Stokes expansion procedure. However, such an approach is of practical value only under restricted conditions, as in the case of anundisturbed wave train described by Stokes second-order theory. In particular, nonlinear wave effects are expected to be of greatest importance for steep shallower waves, and these are precisely the conditions in which a Stokes second-order solution becomes invalid. A numerical solution to the complete boundary value problem without any wave height perturbation procedure is clearly desirable. The approach outlined here is described in detail by Isaacson.4 In this method, the wave diffraction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident wave form approaching the structure. The development of the flow then can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any one instant is obtained by an integral equation method basedon Green's theorem. Comparison with known diffraction solutions can be made only for relatively restricted situations. A few such comparisons have been carried out and arequite favorable. Results also are presented for a typical design wave in shallow water, and these are found to differ significantly from linear theory predictions.

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