scholarly journals Third-order theory for multi-directional irregular waves

2012 ◽  
Vol 698 ◽  
pp. 304-334 ◽  
Author(s):  
Per A. Madsen ◽  
David R. Fuhrman
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Transfer Functions ◽  
Order Theory ◽  
Irregular Waves ◽  
Third Order ◽  
Finite Water Depth ◽  
Wave Trains ◽  
Harmonic Resonance

AbstractA new third-order solution for multi-directional irregular water waves in finite water depth is presented. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential. Expressions for the velocity potential at the free surface are also provided, and the formulation incorporates the effect of an ambient current with the option of specifying zero net volume flux. Harmonic resonance may occur at third order for certain combinations of frequencies and wavenumber vectors, and in this situation the perturbation theory breaks down due to singularities in the transfer functions. We analyse harmonic resonance for the case of a monochromatic short-crested wave interacting with a plane wave having a different frequency, and make long-term simulations with a high-order Boussinesq formulation in order to study the evolution of wave trains exposed to harmonic resonance.

scholarly journals Nonlinear probability distributions of waves in bimodal following and crossing seas generated in laboratory experiments

2013 ◽  
Vol 1 (5) ◽  
pp. 5403-5452
Author(s):  
P. G. Petrova ◽  
C. Guedes Soares
Keyword(s):  
Water Waves ◽  
Probability Distributions ◽  
Spectral Characteristics ◽  
Order Effects ◽  
Wave Interactions ◽  
Third Order ◽  
Empirical Distributions ◽  
Wave Effects ◽  
Wave Trains ◽  
Large Coefficient

Abstract. This paper presents an analysis of the nonlinear distributions of crests, troughs and heights of deep water waves from mixed following sea states generated mechanically in an offshore basin and compares with previous results for mixed crossing seas from the same experiment. The random signals at the wavemaker in both types of mixed seas are characterized by bimodal spectra following the model of Guedes Soares (1984). In agreement with the Benjamin–Feir mechanism, the high-frequency spectrum shows decrease of the peak magnitude and downshift of the peak with the distance, as well as reduction of the tail. The observed statistics and probabilistic distributions exhibit, in general, increasing effects of third-order nonlinearity with the distance from the wavemaker. However, this effect is less pronounced in the wave systems with two following wave trains than in the crossing seas with identical initial spectral characteristics. The relevance of third-order effects due to free modes only is demonstrated and assessed by excluding the vertically asymmetric distortions induced by bound-wave effects of second and third order. The fact that for records characterized by relatively large coefficient of kurtosis, the empirical distributions for the non-skewed profiles continue deviating from the linear predictions, corroborate the relevance of free-wave interactions and thus the need of using higher-order models for the description of wave data.

Third-order theory for bichromatic bi-directional water waves

2006 ◽  
Vol 557 ◽  
pp. 369 ◽  
Author(s):  
PER A. MADSEN ◽  
DAVID R. FUHRMAN
Keyword(s):  
Water Waves ◽  
Order Theory ◽  
Third Order

scholarly journals Distributions of nonlinear wave amplitudes and heights from laboratory generated following and crossing bimodal seas

2014 ◽  
Vol 14 (5) ◽  
pp. 1207-1222 ◽  
Author(s):  
P. G. Petrova ◽  
C. Guedes Soares
Keyword(s):  
High Frequency ◽  
Water Waves ◽  
Order Effects ◽  
Wave Interactions ◽  
Third Order ◽  
Empirical Distributions ◽  
Wave Effects ◽  
Wave Trains ◽  
Large Coefficient ◽  
Higher Order Models

Abstract. This paper presents an analysis of the distributions of nonlinear crests, troughs and heights of deep water waves from mixed following sea states generated mechanically in an offshore basin and compares with previous results for mixed crossing seas from the same experiment. The random signals at the wavemaker in both types of mixed seas are characterized by bimodal spectra following the model of Guedes Soares (1984). In agreement with the Benjamin–Feir mechanism, the high-frequency spectrum shows a decrease in the peak magnitude and downshift of the peak with the distance, as well as reduction of the tail. The observed statistics and probabilistic distributions exhibit, in general, increasing effects of third-order nonlinearity with the distance from the wavemaker. However, this effect is less pronounced in the wave systems with two following wave trains than in the crossing seas, given that they have identical initial characteristics of the bimodal spectra. The relevance of third-order effects due to free modes only is demonstrated and assessed by excluding the vertically asymmetric distortions induced by bound wave effects of second and third order. The fact that for records characterized by relatively large coefficient of kurtosis, the empirical distributions for the non-skewed profiles continue deviating from the linear predictions, corroborate the relevance of free wave interactions and thus the need of using higher-order models for the description of wave data.

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

Structural Safety Assessment of a 1100 TEU Container Ship, Based on a Enhanced Long Term Fatigue Analysis

2014 ◽  
Vol 1036 ◽  
pp. 935-940
Author(s):  
Leonard Domnisoru ◽  
Ionica Rubanenco ◽  
Mihaela Amoraritei
Keyword(s):  
Safety Assessment ◽  
Safety Evaluation ◽  
Irregular Waves ◽  
Structural Safety ◽  
Random Wave ◽  
Wave Loads ◽  
Strength Assessment ◽  
Integrated Method ◽  
Hydroelastic Response

This paper is focused on an enhanced integrated method for structural safety assessment of maritime ships under extreme random wave loads. In this study is considered an 1100 TEU container test ship, with speed range 0 to 18 knots. The most comprehensive criteria for ships structural safety evaluation over the whole exploitation life is based on the long term ship structures analysis, that includes: stress hot-spots evaluation by 3D/1D-FEM hull models, computation of short term ship dynamic response induced by irregular waves, long term fatigue structure assessment. The analysis is enhanced by taking into account the ships speed influence on hydroelastic response. The study includes a comparative analysis on two scenarios for the correlation between the ships speed and waves intensity. The standard constant ship speed scenario and CENTEC scenario, with total speed loss at extreme waves condition, are considered. Instead of 20 years ship exploitation life estimated by classification societies rules from the long term structural safety criteria, the enhanced method has predicted more restrictive values of 14.4-15.7 years. The numerical analyses are based on own software and user subroutines. The study made possible to have a more realistic approach of ships structural strength assessment, for elastic and faster ships as container carriers, in compare to the standard one based only on naval rules, delivering a method with higher confidence in the designed structural safety.

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

2016 ◽  
Vol 60 (03) ◽  
pp. 145-155
Author(s):  
Ya-zhen Du ◽  
Wen-hua Wang ◽  
Lin-lin Wang ◽  
Yu-xin Yao ◽  
Hao Gao ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Linear Response Theory ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Loads ◽  
Floating Bodies ◽  
Drift Motion ◽  
First Order ◽  
Series Of Experiments ◽  
Deck Wetness

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

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