Aspects of Nonlinear Random Wave Kinematics

2002 ◽  
Author(s):  
Dag Myrhaug ◽  
Carl Trygve Stansberg ◽  
Hanne Therese Wist
Keyword(s):  
Free Surface ◽  
Second Order ◽  
Difference Frequency ◽  
Stokes Wave ◽  
Frequency Effect ◽  
Random Wave ◽  
Sum Frequency ◽  
Wave Kinematics ◽  
Nonlinear Random Wave ◽  
Nonlinear Free Surface

Statistics of the nonlinear free surface elevation as well as the nonlinear random wave kinematics in terms of the horizontal velocity component in arbitrary water depth are addressed. Two different methods are considered: a simplified analytical approach based on second-order Stokes wave theory including the sum-frequency effect only, and a second-order random wave model including both sum-frequency and difference-frequency effects. The paper compares results for the statistics of the nonlinear free surface, and the consequences of neglecting the difference-frequency effect in the first method are discussed.

Nonlinear Wave Disturbance Around a Vertical Circular Column

2002 ◽  
Author(s):  
C. T. Stansberg ◽  
H. Braaten
Keyword(s):  
Linear Prediction ◽  
Harmonic Component ◽  
Nonlinear Effects ◽  
Second Order ◽  
Wave Disturbance ◽  
Difference Frequency ◽  
Irregular Waves ◽  
Order Effects ◽  
Sum Frequency ◽  
Circular Column

The wave disturbance close to vertical columns is analysed. In particular, the deviations from linear predictions are investigated, by experimental as well as by numerical methods. Thus a second-order numerical diffraction model is established by means of a diffraction analysis code (WAMIT) and compared to model tests with a single, fixed column with diameter 16m. Tests in regular, bi-chromatic as well as irregular waves are run. Significant nonlinear effects are observed, especially in steep waves, with the maximum elevation in front of the column increasing from 11.5m in a linear prediction to around 19m, in a 12s regular wave with 22m wave height. The main nonlinear effects in front of the column are identified as second-order sum-frequency and difference-frequency terms, plus a significant nonlinear increase in the first harmonic component. The WAMIT prediction of the second-order effects agrees fairly well with the measurements, although with some overprediction and underprediction, respectively, of the sum-frequency and difference-frequency (LF and mean set-up) terms in the steepest waves. For the underprediction of the first harmonic, however, a theory beyond second order is required.

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.

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.

Nonlinear Space–Time Evolution of Wave Groups With a High Crest

2005 ◽  
Vol 127 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Felice Arena ◽  
Francesco Fedele
Keyword(s):  
Time Evolution ◽  
Surface Displacement ◽  
Fixed Time ◽  
Space Time ◽  
Second Order ◽  
Random Wave ◽  
Wave Groups ◽  
Free Surface Displacement ◽  
Nonlinear Free Surface ◽  
Space Time Evolution

The theory of quasi-determinism, for the mechanics of linear random wave groups was obtained by Boccotti in the eighties. The first formulation of the theory deals with the largest crest amplitude; the second formulation deals with the largest wave height. In this paper the first formulation of Boccotti’s theory, particularized for long-crested waves, is extended to the second-order. The analytical expressions of the nonlinear free surface displacement and velocity potential are obtained. The space–time evolution of the nonlinear wave group, when a very large crest occurs at a fixed time and location, is then shown. Finally the second-order probability of exceedance of the crest amplitude is obtained and validated by Monte Carlo simulation.

Time-Domain Simulation of Second-Order Wave Diffraction in Irregular Wave

2012 ◽  
Author(s):  
Gang Xu ◽  
A. M. S. Hamouda
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Wave Diffraction ◽  
Second Order ◽  
Stokes Wave ◽  
Surface Boundary ◽  
Time Domain Simulation ◽  
Zone Method ◽  
Body Interaction ◽  
Irregular Wave

A time-domain second-order method is presented to simulate three-dimensional (3D) wave-body interaction. In the approach, Taylor series expansions are applied to the free surface boundary conditions, and Stokes perturbation procedure is then used to establish corresponding boundary value problem at first-order and second-order on the time-independent surfaces. A Boundary Element Method (BEM), based on Rankine source, is used to calculate wave field at each time step. Multi-Transmitting Formula coupled with Damping Zone method (MTF+DZ) is employed as radiation condition to minimize the wave reflection. A stable Integral form of Free surface Boundary Condition (IFBC) is used to update velocity potential on the free surface. The present method is applied to compute the second-order Stokes wave diffraction of bottom-mounted circular cylinder first, and then to compute the irregular second-order Stokes wave diffraction of truncated cylinder in infinite water depth with three wave components. It is shown that long time simulation can be done with stability, and the model can be used to time-domain simulation of nonlinear irregular wave-body interaction.

Kinematics Under Extreme Waves

2006 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Ove T. Gudmestad ◽  
Sverre K. Haver
Keyword(s):  
Free Surface ◽  
Water Level ◽  
Linear Prediction ◽  
Laboratory Data ◽  
Wave Model ◽  
Relative Magnitude ◽  
Second Order ◽  
Random Wave ◽  
Extreme Waves ◽  
Particle Velocities

Four different methods for prediction of wave-zone particle velocities under steep crests in random seas are compared. The study includes linear prediction, a second-order random wave model, Wheeler’s method, and a new method proposed by Grue et al. (2003). Comparison to laboratory data is also made. The purpose is to observe and evaluate differences in predictions for high and extreme waves, and how well they agree with measurements. The whole range from below still water level up to the free surface is considered. It is found that the second-order random wave model works best at all levels of the water column under a steep crest in deep water, and is therefore recommended. Grue’s method works reasonably well in many cases for z > 0, i.e. above the calm water level, but it overpredicts the velocities for z < 0. Wheeler’s method, when used with a measured or a second-order input elevation record, predicts fairly well the velocities at the free surface z = ηmax, but it underpredicts around z = 0 as well as at lower levels. The relative magnitude of this underprediction is slightly lower than the local steepness kA0 and can be quite significant in extreme waves. If Wheeler’s method is used with a linear input, the same error occurs also at the free surface.

Review of Approximations to Evaluate Second-Order Low-Frequency Load

2012 ◽  
Author(s):  
Guillaume de Hauteclocque ◽  
Flávia Rezende ◽  
Olaf Waals ◽  
Xiao-Bo Chen
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Low Frequency ◽  
Second Order ◽  
The Body ◽  
Difference Frequency ◽  
Surface Boundary ◽  
First Order ◽  
Potential Part ◽  
The Difference

The second order low-frequency loads are one of main sources of excitation for moored systems. These loads are usually decomposed into the quadratic part, contributed only by first order quantities and potential part contributed by the second order potentials. In shallow water the second order incoming and diffracted potentials give a significant contribution to the low frequency forces. Therefore, the accuracy on the determination of this parcel of the low-frequency loads is a key issue for the assessment of mooring lines and operability of systems moored in shallow water area, as for example LNG terminals. Due to the complexity in computing the second order diffraction potential, which would involve a non-homogeneous free surface boundary condition, the so-called Pinkster approximation has been proposed. This approximation is based on the assumption that the major contribution to the potential part of low-frequency loads is given by the second order potential of the undisturbed incoming waves. The methods to compute the wave forces related to the second order potentials are based on scaling of the first order wave induced forces. Another approximation recently formulated in Chen and Rezende consists of developing the second-order bi-frequency load into a series of different orders of the difference frequency. The potential contribution to the term proportional to the difference-frequency can be evaluated efficiently by involving an integral over a small zone on the free surface around the body. In the present paper, the existing approximations are revisited and compared to analytical solution of exact second-order load on a vertical cylinder and for the case of floating body (LNG) in shallow water. Some guidelines in the practical use of different approximations will be derived.

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