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

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.

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.

Statistical Analysis of a Set of Basin Waves

2011 ◽  
Author(s):  
Jule Scharnke ◽  
Janou Hennig
Keyword(s):  
Statistical Analysis ◽  
Wave Height ◽  
Water Depth ◽  
Water Waves ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Distribution Functions ◽  
Wave Crest ◽  
Intermediate Water ◽  
Wave Measurements

In a recent paper the effect of variations in calibrated wave parameters on wave crest and height distributions was analyzed (OMAE2010-20304, [1]). Theoretical distribution functions were compared to wave measurements with a variation in water depth, wave seed (group spectrum) and location of measurement for the same initial power spectrum. The wave crest distribution of the shallow water waves exceeded both second-order and Rayleigh distribution. Whereas, in intermediate water depth the measured crests followed the second order distribution. The distributions of the measured waves showed that different wave seeds result in the same wave height and crest distributions. Measured wave heights were lower closer to the wave maker. In this paper the results of the continued statistical analysis of basin waves are presented with focus on wave steepness and their influence on wave height and wave crest distributions. Furthermore, the sampling variability of the presented cases is assessed.

New Insights in Extreme Crest Height Distributions: A Summary of the ‘CresT’ JIP

2011 ◽  
Author(s):  
Bas Buchner ◽  
George Forristall ◽  
Kevin Ewans ◽  
Marios Christou ◽  
Janou Hennig
Keyword(s):  
Single Point ◽  
Field Measurements ◽  
Order Theory ◽  
Second Order ◽  
Wave Crest ◽  
Height Distribution ◽  
Extreme Waves ◽  
Wave Height Distribution ◽  
Floating Platforms ◽  
Crest Height

The objective of the CresT JIP was ‘to develop models for realistic extreme waves and a design methodology for the loading and response of floating platforms’. Within this objective the central question was: ‘What is the highest (most critical) wave crest that will be encountered by my platform in its lifetime?’ Based on the presented results for long and short-crested numerical, field and basin results in the paper, it can be concluded that the statistics of long-crested waves are different than those of short-crested waves. But also short-crested waves show a trend to reach crest heights above second order. This is in line with visual observations of the physics involved: crests are sharper than predicted by second order, waves are asymmetric (fronts are steeper) and waves are breaking. Although the development of extreme waves within short-crested sea states still needs further investigation (including the counteracting effect of breaking), at the end of the CresT project the following procedure for taking into account extreme waves in platform design is recommended: 1. For the wave height distribution, use the Forristall distribution (Forristall, 1978). 2. For the crest height distribution, use 2nd order distribution as basis. 3. Both the basin and field measurements show crest heights higher than predicted by second order theory for steeper sea states. It is therefore recommended to apply a correction to the second order distribution based on the basin results. 4. Account for the sampling variability at the tail of the distribution (and resulting remaining possibility of higher crests than given by the corrected second order distribution) in the reliability analysis. 5. Consider the fact that the maximum crest height under a complete platform deck can be considerably higher than the maximum crest at a single point.

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 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.

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 Crest Height Distribution in Three-Dimensional Ocean Waves

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Felice Arena ◽  
Alfredo Ascanelli
Keyword(s):  
Water Depth ◽  
Three Dimensional ◽  
Ocean Waves ◽  
Order Theory ◽  
Second Order ◽  
Wave Crest ◽  
Height Distribution ◽  
Random Waves ◽  
Weakly Nonlinear ◽  
Wave Trough

The interest and 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 the Rayleigh law. In this paper, a theoretical crest distribution is obtained, taking into account the extension of Boccotti’s quasideterminism theory (1982, “On Ocean Waves With High Crests,” Meccanica, 17, pp. 16–19), up to the second order for the case of three-dimensional waves in finite water depth. To this purpose, the Fedele and Arena (2005, “Weakly Nonlinear Statistics of High Random Waves,” Phys. Fluids, 17(026601), pp. 1–10) distribution is generalized to three-dimensional waves on an arbitrary water depth. The comparison with Forristall’s second order model (2000, “Wave Crest Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr., 30(8), pp. 1931–1943) 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 the long-crested model.

scholarly journals Nonlinear Wave Kinematics near the Ocean Surface

2017 ◽  
Vol 47 (7) ◽  
pp. 1657-1673 ◽  
Author(s):  
P. B. Smit ◽  
T. T. Janssen ◽  
T. H. C. Herbers
Keyword(s):  
Ocean Surface ◽  
Second Order ◽  
Transport Processes ◽  
Inviscid Fluid ◽  
Random Waves ◽  
Usual Practice ◽  
Near Surface ◽  
Wave Kinematics ◽  
Highly Nonlinear ◽  
Surface Kinematics

AbstractEstimation of second-order, near-surface wave kinematics is important for interpretation of ocean surface remote sensing and surface-following instruments, determining loading on offshore structures, and understanding of upper-ocean transport processes. Unfortunately, conventional wave theories based on Stokes-type expansions do not consider fluid motions at levels above the unperturbed fluid level. The usual practice of extrapolating the fluid kinematics from the unperturbed free surface to higher points in the fluid is generally reasonable for narrowband waves, but for broadband ocean waves this results in dramatic (and nonphysical) overestimation of surface velocities. Consequently, practical approximations for random waves are at best empirical and are often only loosely constrained by physical principles. In the present work, the authors formulate the governing equations for water waves in an incompressible and inviscid fluid, using a boundary-fitted coordinate system (i.e., sigma or s coordinates) to derive expressions for near-surface kinematics in nonlinear random waves from first principles. Comparison to a numerical model valid for highly nonlinear waves shows that the new results 1) are consistent with second-order Stokes theory, 2) are similar to extrapolation methods in narrowband waves, and 3) greatly improve estimates of surface kinematics in random seas.

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