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.

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.

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.

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.

Linear Evolution of a Narrow-Banded Surface Gravity Wavepacket Over an Infinite Step

2019 ◽  
Author(s):  
Yan Li ◽  
Thomas A. A. Adcock ◽  
Ton S. van den Bremer
Keyword(s):  
Water Depth ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Fundamental Problem ◽  
Wave Theory ◽  
Second Order ◽  
Order Effects ◽  
Linear Evolution ◽  
Finite Water Depth ◽  
Higher Order Effects

Abstract This paper focuses on the classical and fundamental problem of waves propagating over an infinite step in finite water depth. Specifically, this paper aims to extend classical narrow-banded wave theory for constant water depth which uses a multiple-scales expansion to the case of an abrupt change in the water depth, known as an infinite step. This paper derives the linear evolution equations and is the first step towards the calculation of second-order and higher-order effects for wavepackets travelling over a step using commonly employed envelope-type evolution equations, in particular the bound sub- and super-harmonics at second order.

scholarly journals Experimental particle paths and drift velocity in steep waves at finite water depth

2016 ◽  
Vol 810 ◽  
Author(s):  
John Grue ◽  
Jostein Kolaas
Keyword(s):  
Drift Velocity ◽  
Water Depth ◽  
Order Theory ◽  
Second Order ◽  
Velocity Shear ◽  
Vertical Position ◽  
Functional Relationships ◽  
Finite Water Depth ◽  
Particle Paths ◽  
Experimental Particle

The Lagrangian paths, horizontal Lagrangian drift velocity, $U_{L}$, and the Lagrangian excess period, $T_{L}-T_{0}$, where $T_{L}$ is the Lagrangian period and $T_{0}$ the Eulerian linear period, are obtained by particle tracking velocimetry (PTV) in non-breaking periodic laboratory waves at a finite water depth of $h=0.2~\text{m}$, wave height of $H=0.49h$ and wavenumber of $k=0.785/h$. Both $U_{L}$ and $T_{L}-T_{0}$ are functions of the average vertical position of the paths, $\bar{Y}$, where $-1<\bar{Y}/h<0$. The functional relationships $U_{L}(\bar{Y})$ and $T_{L}-T_{0}=f(\bar{Y})$ are very similar. Comparisons to calculations by the inviscid strongly nonlinear Fenton method and the second-order theory show that the streaming velocities in the boundary layers below the wave surface and above the fluid bottom contribute to a strongly enhanced forward drift velocity and excess period. The experimental drift velocity shear becomes more than twice that obtained by the Fenton method, which again is approximately twice that of the second-order theory close to the surface. There is no mass flux of the periodic experimental waves and no pressure gradient. The results from a total number of 80 000 experimental particle paths in the different phases and vertical positions of the waves show a strong collapse. The particle paths are closed at the two vertical positions where $U_{L}=0$.

Burial and Scour of Short Cylinders and Truncated Cones Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Currents

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Muk Chen Ong ◽  
Dag Myrhaug
Keyword(s):  
Narrow Band ◽  
Three Dimensional ◽  
Wave Crest ◽  
Height Distribution ◽  
Random Waves ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D ◽  
The Waves ◽  
Crest Height

This paper provides a practical stochastic method by which the burial and scour depths of short cylinders and truncated cones exposed to long-crested (two-dimensional (2D)) and short-crested (three-dimensional (3D)) nonlinear random waves plus currents can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall second-order wave crest height distribution representing both 2D and 3D nonlinear random waves. Moreover, the formulas for the burial and the scour depths for regular waves plus currents presented by previous published work for short cylinders and truncated cones are used.

Three-Dimensional Numerical Calculations of a Jet in an External Cross Flow: Application to Pollutant Dispersion

2003 ◽  
Vol 125 (3) ◽  
pp. 510-522 ◽  
Author(s):  
Nejla Mahjoub Said ◽  
Hatem Mhiri ◽  
Salem El Golli ◽  
Georges Le Palec ◽  
Philippe Bournot
Keyword(s):  
Three Dimensional ◽  
Cross Flow ◽  
Pollutant Dispersion ◽  
Scalar Fields ◽  
Second Order ◽  
Turbulent Jet ◽  
Dimensional Structure ◽  
Order Model ◽  
Air Stream ◽  
Helium Jet

The paper presents a three-dimensional numerical simulation of a circular turbulent jet issuing transversely into a uniform air stream. In the first part an air-helium jet is considered and the three-dimensional structure of the flow field is discussed. Then, a comparison between the numerical results of four turbulence closure models (three first-order models and a second-order one) are presented and compared with the experimental data given by Crabb et al. [7] and Andreopoulos et al. [9]. Although the different models render identical results in the upstream and far downstream regions of the jet, only the second order model is shown to give good results in the exit region and in the trailing zone of the jet. Based on this last model, the dynamic and scalar fields of a fume turbulent jet issuing transversely with velocity v0 into a uniform air flow with velocity u are then examined as functions of the ratio R=v0/u∞ in order to simulate pollutant dispersion from industrial chimneys.

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