Conditional Short-Crested Second Order Waves in Shallow Water and With Superimposed Current

2004 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Shallow Water ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Second Order ◽  
Stokes Wave ◽  
Wave Crest ◽  
Wave Kinematics ◽  
Wave Approach ◽  
Non Linear

For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected second order short-crested wave riding on a uniform current is given. The analysis is based on the second order Sharma and Dean shallow water wave theory and the direction of the main wind direction can make any direction with the current. Numerical results showing the importance of the water depth, the directional spreading and the current on the conditional mean wave profile and the associated wave kinematics are presented. A discussion of the use of the conditional wave approach as design waves is given.

Conditional Short-Crested Waves in Shallow Water and With Superimposed Current

2002 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Wave Spectrum ◽  
Wave Theory ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Stokes Wave ◽  
Wave Crest ◽  
Non Linear ◽  
Drilling Rigs

For bottom-supported offshore structures like oil drilling rigs and oil production platforms, a deterministic design wave approach is often applied using a regular non-linear Stokes’ wave. Thereby, the procedure accounts for non-linear effects in the wave loading but the randomness of the ocean waves is poorly represented, as the shape of the wave spectrum does not enter the wave kinematics. To overcome this problem and still keep the simplicity of a deterministic approach, Tromans, Anaturk and Hagemeijer (1991) suggested the use of a deterministic wave, defined as the expected linear Airy wave, given the value of the wave crest at a specific point in time or space. In the present paper a derivation of the expected linear short-crested wave riding on a uniform current is given. The analysis is based on the conventional shallow water Airy wave theory and the direction of the main wind direction can make any direction with the current. A consistent derivation of the wave spectrum taking into account current and finite water depth is used. The numerical results show a significant effect of the water depth, the directional spreading and the current on the conditional mean wave profile. Extensions to higher order waves are finally discussed.

Nonlinear Crest Height Distribution in Three-Dimensional Ocean Waves

2008 ◽  
Author(s):  
Felice Arena ◽  
Alfredo Ascanelli
Keyword(s):  
Water Depth ◽  
Three Dimensional ◽  
Ocean Waves ◽  
Second Order ◽  
Wave Crest ◽  
Height Distribution ◽  
Order Model ◽  
Rayleigh Law ◽  
Wave Trough ◽  
Finite Water Depth

The interest and the studies on nonlinear waves are increased recently for their importance in the interaction with floating and fixed bodies. It is also well known that nonlinearities influence wave crest and wave trough distributions, both deviating from Rayleigh law. In this paper a theoretical crest distribution is obtained taking into account the extension of Boccotti’s Quasi Determinism theory, up to the second order for the case of three-dimensional waves, in finite water depth. To this purpose the Fedele & Arena [2005] distribution is generalized to three-dimensional waves on an arbitrary water depth. The comparison with Forristall second order model shows the theoretical confirmation of his conclusion: the crest distribution in deep water for long-crested and short crested waves are very close to each other; in shallow water the crest heights in three dimensional waves are greater than values given by long-crested model.

Flexible Riser Response Induced by Springing of an FPSO Hull

2007 ◽  
Author(s):  
Jelena Vidic-Perunovic ◽  
Niels J. Risho̸j Nielsen ◽  
Haiwen Zhang
Keyword(s):  
High Frequency ◽  
Wave Spectrum ◽  
Analytical Form ◽  
Second Order ◽  
Wave Frequency ◽  
Natural Vibration Frequency ◽  
Linear Wave ◽  
Flexible Riser ◽  
Excitation Wave ◽  
Non Linear

The hydrodynamic analysis of the flexible riser for offshore application is usually limited to the first order wave frequency motions of the floating vessel that holds the riser top end. In this paper effort is made to investigate the influence of non-linear second order springing deflection of the production vessel hull on flexible riser response. The system selected in this study consists of a free-hanging flexible riser configuration attached to an FPSO. Due to resonance between the excitation wave frequency and the natural vibration frequency of the hull, second order flexible vertical motions of the FPSO increase. This may influence the riser loads, presumably the tension force. Vertical motions including the second order high frequency contribution are assigned to the flexible riser at a point of attachment to the vessel. To account for the environmental loading, irregular sea is applied, characterized by modified linear wave spectrum. Second order excitation wave spectrum is truncated by use of WAFO routines for random second order wave simulation and an analytical form of the spectrum that accounts for the non-linear wave effects is proposed. Several environmental conditions are examined in order to consolidate the tendency in riser behaviour. The significance of the high-frequency quadratic terms in the loads along the flexible riser is discussed.

Influence of Wave Group Characteristics on the Motion of a Semisubmersible in Freak Waves

2014 ◽  
Author(s):  
Yanfei Deng ◽  
Jianmin Yang ◽  
Longfei Xiao
Keyword(s):  
Time Lag ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Hydrodynamic Performance ◽  
Wave Crest ◽  
Time Lags ◽  
Wave Group ◽  
Freak Waves ◽  
Motion Responses ◽  
Group Characteristics

In the last few decades, the hydrodynamic performance of offshore structures has been widely studied to ensure their safety as well as to achieve an economical design. However, an increasing number of reported accidents due to rough ocean waves call for in-depth investigations on the loads and motions of offshore structures, particularly the effect of freak waves. The aim of this paper is to determine the sea conditions that may cause the maximum motion responses of offshore structures, which have a significant effect on the loads of mooring systems because of their tight relationship. As a preliminary step, the response amplitude operators (RAOs) of a semisubmersible platform of 500 meters operating depth are obtained with the frequency-domain analysis method. Subsequently, a series of predetermined extreme wave sequences with different wave group characteristics, such as the maximum crest amplitude and the time lag between successive high waves, are adopted to calculate the hydrodynamic performance of the semisubmersible with mooring systems in time-domain. The paper shows that the maximum motion responses not only depend on the largest wave crest amplitude but also the time lags between successive giant waves. This paper will provide an important reference for future designs which could consider the most dangerous wave environment.

Hydrodynamic Modeling of Large-Diameter Bottom-Fixed Offshore Wind Turbines

2015 ◽  
Author(s):  
Erin E. Bachynski ◽  
Harald Ormberg
Keyword(s):  
Wind Turbines ◽  
Environmental Conditions ◽  
Limit State ◽  
Second Order ◽  
Offshore Wind ◽  
Stokes Wave ◽  
Intermediate Water ◽  
Hydrodynamic Loads ◽  
Offshore Wind Turbines ◽  
Wave Kinematics

For shallow and intermediate water depths, large monopile foundations are considered to be promising with respect to the levelized cost of energy (LCOE) of offshore wind turbines. In order to reduce the LCOE by structural optimization and de-risk the resulting designs, the hydrodynamic loads must be computed efficiently and accurately. Three efficient methods for computing hydrodynamic loads are considered here: Morison’s equation with 1) undisturbed linear wave kinematics or 2) undisturbed second order Stokes wave kinematics, or 3) the MacCamy-Fuchs model, which is able to account for diffraction in short waves. Two reference turbines are considered in a simplified range of environmental conditions. For fatigue limit state calculations, accounting for diffraction effects was found to generally increase the estimated lifetime of the structure, particularly the tower. The importance of diffraction depends on the environmental conditions and the structure. For the case study of the NREL 5 MW design, the effect could be up to 10 % for the tower base and 2 % for the monopile under the mudline. The inclusion of second order wave kinematics did not have a large effect on the fatigue calculations, but had a significant impact on the structural loads in ultimate limit state conditions. For the NREL 5 MW design, a 30 % increase in the maximum bending moment under the mudline could be attributed to the second order wave kinematics; a 7 % increase was seen for the DTU 10 MW design.

Simplified Method to Assess Dynamic Response of Jacket Type Offshore Platforms Subjected to Wave Loading

2004 ◽  
Author(s):  
B. Asgarian ◽  
A. Mohebbinejad ◽  
R. H. Soltani
Keyword(s):  
Dynamic Response ◽  
Dynamic Characteristics ◽  
Offshore Structures ◽  
Center Of Gravity ◽  
Simplified Model ◽  
Mode Shapes ◽  
Stokes Wave ◽  
Wave Crest ◽  
Offshore Platforms ◽  
Wave Loading

Dynamic response of offshore platforms subjected to wave and current is of fundamental importance in analysis. The first step in dynamic analysis is computing dynamic characteristics of the structure. Because of pile-soil-structure and fluid-structure interactive effects in the dynamic behavior, the model is very complex. In this paper a simplified model for dynamic response of jacket-type offshore structures subjected to wave loading is used. Since wave loads on offshore platforms vary with time, they produce dynamic effects on structures. In the model used in this paper, all of the structural elements are modeled as vertical equivalent cylinders that are in the direction of the wave crest. In the simplified model, the degrees of freedom are considered at the seabed, jacket horizontal elevations and topside center of gravity. The stiffness properties of the model are computed considering the stiffnesses of the vertical bracings, legs and piles. The structural mass is considered as lumped nodal masses at horizontal elevations and topside center of gravity. The hydrodynamic added mass in addition to the structural masses was modeled at jacket horizontal elevations. In the simplified model, for computing wave loading, the projected areas of all members in the direction of the wave crest are considered. For the wave loading calculation, Morison equation is considered. The fluid velocities are calculated for the submerged portions of the structures using a computer program developed for this purpose. In this program both Airy and Stokes wave theories can be used. This model can be used to assess dynamic properties and responses of jacket type offshore structures. The model is used to assess the response of three jacket-type offshore platforms in Persian Gulf subjected to loadings due to several waves. The results in terms of dynamic characteristics and responses were compared with the more accurate analysis results using SACS software. The results are in a good agreement with the SACS analysis outputs, i.e. structural periods, mode shapes and dynamic response.

Propagation of Steep and Breaking Short-Crested Waves: A Comparison of CFD Codes

2018 ◽  
Author(s):  
Øystein Lande ◽  
Thomas Berge Johannessen
Keyword(s):  
Wave Propagation ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Practical Reasons ◽  
Breaking Wave ◽  
Linear Wave ◽  
Wave Groups ◽  
Irregular Wave ◽  
Highly Nonlinear

Using the computational fluid domain for propagation of ocean waves have become an important tool for the calculation of highly nonlinear wave loading on offshore structures such as run-up, wave slamming and non-linear breaking wave kinematics. At present, there are many computational fluid dynamics (CFD) codes available which can be employed to calculate water wave propagation and wave induced loading on structures. For practical reasons, however, the use of these codes is often limited to the propagation of regular uni-directional waves initiated very close to the structure, or to investigating the properties and loading due to measured waves by fitting a numerical wave to a measured wave profile. The present paper focuses on the propagation of steep irregular and short crested wave groups up to the point of breaking. Indeed, this is challenging because of the highly nonlinear behavior of irregular wave groups as steepness increases and they approach the point of breaking. The complexity further increases with the introduction of short-crestedness requiring computation in a large 3-dimentional domain. Two CFD codes are used in this comparison study which are believed to be well conditioned for wave propagation, the commercial code ComFLOW (available through the ComFLOW JIP project) and the open-source code BASILISK. The primary objective of this paper to show the two CFD codes capability of recreating measured irregular wave groups, using the known linear wave components from the model test as input to fluid domain. Wave elevation is measured at several locations in the close vicinity of the focus point. The comparison is carried out for a selection of events with variation in steepness, wave spreading and wave spectrum.

Long-period seafloor seismology and deformation under ocean waves

1999 ◽  
Vol 89 (6) ◽  
pp. 1535-1542 ◽  
Author(s):  
Spahr C. Webb ◽  
Wayne C. Crawford
Keyword(s):  
Shallow Water ◽  
Signal To Noise Ratio ◽  
Wave Spectrum ◽  
Vertical Component ◽  
Ocean Waves ◽  
Vertical Acceleration ◽  
Noise Levels ◽  
Signal To Noise ◽  
Long Period ◽  
Noise Ratio

Abstract The deformation of the seafloor under loading by long-period ocean waves raises vertical component noise levels at the deep seafloor by 20 to 30 dB above noise levels at good continental sites in the band from 0.001 to 0.04 Hz. This noise substantially limits the detection threshold and signal-to-noise ratio for long-period phases of earthquakes observed by seafloor seismometers. Borehole installation significantly improves the signal-to-noise ratio only if the sensor is installed at more than 1 km below the seafloor because the deformation signal decays slowly with depth. However, the vertical-component deformation signal can be predicted and suppressed using seafloor measurements of pressure fluctuations observed by differential pressure gauges. The pressure observations of ocean waves are combined with measurements of the transfer function between vertical acceleration and pressure to predict the vertical component deformation signal. Subtracting the predicted deformation signal from pressure observations can reduce vertical component noise levels near 0.01 Hz by more than 25 dB, significantly improving signal-to-noise ratios for long-period phases. There is also a horizontal-component deformation signal but it is smaller than the vertical-component signal and only significant in shallow water (<1-km deep). The amplitude of the deformation signal depends both on the long-period ocean-wave spectrum and the elastic-wave velocities in the oceanic crust. It is largest at sedimented sites and in shallow water.

Second-order wave kinematics conditional on a given wave crest

1996 ◽  
Vol 18 (2-3) ◽  
pp. 119-128 ◽  
Author(s):  
Jørgen Juncher Jensen
Keyword(s):  
Second Order ◽  
Wave Crest ◽  
Wave Kinematics

Nonlinear Wave Calculations for Engineering Applications

2001 ◽  
Vol 124 (1) ◽  
pp. 28-33 ◽  
Author(s):  
George Z. Forristall
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Wave Spectrum ◽  
Computational Cost ◽  
Wave Structure ◽  
Second Order ◽  
Nonlinear Wave Equations ◽  
Wave Crest ◽  
Engineering Applications ◽  
Large Structures

Waves in the ocean are nonlinear, random, and directionally spread, but engineering calculations are almost always made using waves that are either linear and random or nonlinear and regular. Until recently, methods for more accurate computations simply did not exist. Increased computer speeds and continued theoretical developments have now led to tools which can produce much more realistic waves for engineering applications. The purpose of this paper is to review some of these developments. The simplest nonlinearities are the second-order bound waves caused by the pairwise interaction of linear components of the wave spectrum. It is fairly easy to simulate the second-order surface resulting from those interactions, a fact which has recently been exploited to estimate the probability distribution of wave crest heights. Once the evolution of the surface is known, the kinematics of the subsurface flow can be evaluated reasonably easily from Laplace’s equation. Much of the bound wave structure can also be captured by using the Creamer transformation, a definite integral over the spatial domain which modifies the structure of the wave field at one instant in time. In some ways, the accuracy of the Creamer transformation is higher than second order. Finally, many groups have developed numerical wave tanks which can solve the nonlinear wave equations to arbitrary accuracy. The computational cost of these solutions is still rather high, but they can directly calculate potential forces on large structures as well as providing test cases for the less accurate, but more efficient, methods.

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