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.

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.

Measurements of third-order resonant wave interactions

1966 ◽  
Vol 25 (3) ◽  
pp. 437-456 ◽  
Author(s):  
L. F. Mcgoldrick ◽  
O. M. Phillips ◽  
N. E. Huang ◽  
T. H. Hodgson
Keyword(s):  
Gravity Waves ◽  
Resonant Interaction ◽  
Experimental Demonstration ◽  
Wave Interactions ◽  
Third Order ◽  
The Third ◽  
Resonant Wave ◽  
Interaction Distance ◽  
At Resonance ◽  
Wave Trains

This paper presents the results of experiments on the resonant interaction of gravity waves. Two mutually-orthogonal primary wave trains are generated in a tank and their interaction products studied at various positions on the surface. Under suitable conditions, the growing resonant third-order interaction product is identified; its amplitude is shown to be a linear function of the interaction distance. The band-width of the response decreases with increasing distance, as is characteristic of the phenomenon of resonance. The ratio of the frequencies of the primary waves at resonance is very close to that predicted theoretically; the growth rate of the third component is close to, though about 20% higher than, the predicted value. Conditions far from resonance are also studied; it is found that the growing tertiary wave is absent in this case.These results offer the first unambiguous experimental demonstration of resonant wave interactions.

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.

Statistics of Nonlinear Waves Simulated in a Wave Basin

2009 ◽  
Author(s):  
Zhivelina Cherneva ◽  
M. Aziz Tayfun ◽  
C. Guedes Soares
Keyword(s):  
Nonlinear Waves ◽  
Water Waves ◽  
Nonlinear Interactions ◽  
Third Order ◽  
Empirical Distributions ◽  
Upper Limits ◽  
Wave Basin ◽  
Propagating Waves ◽  
Wave Heights ◽  
Modulational Instabilities

Modulational instabilities induced by third-order nonlinear interactions among freely propagating waves can cause the statistics of various surface features to deviate significantly from the predictions based on the linear Gaussian and second-order models. This study analyzes deep-water waves simulated in a wave basin and characterized with such instabilities, and compares the statistics of the wave heights, crests and troughs amplitudes observed with a variety of theoretical approximations based on Gram-Charlier expansions. The results indicate that the theoretical approximations describe the empirical distributions observed reasonably well, for the most part. Further comparisons also show that the heights and crests of the largest waves do not exceed Miche-Stokes type upper limits.

scholarly journals Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance

2014 ◽  
Vol 1 (2) ◽  
pp. 1539-1602 ◽  
Author(s):  
C. A. L. Pires ◽  
R. A. P. Perdigão
Keyword(s):  
Resonance Condition ◽  
Probability Distributions ◽  
Optimization Method ◽  
Statistical Dependence ◽  
Third Order ◽  
Interaction Information ◽  
Wave Resonance ◽  
Wave Trains ◽  
Non Gaussian ◽  
Nonlinear Correlations

Abstract. Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross cumulants. Its application to a minimal one-dimensional, periodic, advective model, leads to enhanced triads that occur between oscillating components of circular or locally confined wave-trains satisfying the triadic wave resonance condition.

Nonlinear Wave Statistics

2010 ◽  
Author(s):  
Francesco Fedele ◽  
Zhivelina Cherneva ◽  
M. Aziz Tayfun ◽  
Carlos Guedes Soares
Keyword(s):  
Water Waves ◽  
Spectral Characteristics ◽  
Third Order ◽  
Large Wave ◽  
Wave Statistics ◽  
Spectral Changes ◽  
Resonant Interactions ◽  
Surface Displacements ◽  
Wave Basin ◽  
Modulational Instabilities

Third-order quasi-resonant interactions among free waves and associated modulational instabilities can significantly affect the statistics of various surface features in narrowband waves. In particular, modulational instabilities tend to induce intermittent amplifications on the surface displacements, causing their statistics to deviate from the linear Gaussian and second order models. Herein, we investigate the nature of such instabilities on the statistical and spectral characteristics of deep-water waves generated in a large wave basin. We analyze the spectral changes that occur as waves propagate along the basin, develop bounds on the spectrum bandwidth, and interpret various statistics based on third-order Gram-Charlier distributions.

Effects of wavelength ratio on wave modelling

1993 ◽  
Vol 248 ◽  
pp. 107-127 ◽  
Author(s):  
Jun Zhang ◽  
Keyyong Hong ◽  
Dick K. P. Yue
Keyword(s):  
Wave Model ◽  
Short Wave ◽  
Wave Mode ◽  
The Other ◽  
Wave Steepness ◽  
Wave Interactions ◽  
Third Order ◽  
Long Wavelength ◽  
Modulated Phase ◽  
Wave Trains

The efficacy of perturbation approaches for short–long wave interactions is examined by considering a simple case of two interacting wave trains with different wavelengths. Frequency-domain solutions are derived up to third order in wave steepness using two different formulations: one employing conventional wave-mode functions only, and the other introducing a modulated wave-mode representation for the short-wavelength wave. For long-wavelength wave steepness and short-to-long wavelength ratio ε1 and ε3 respectively, the two results are shown to be identical for ε1 [Lt ] ε3 < 0.5. As ε1 approaches ε3, the conventional wave-mode approach converges slowly and eventually diverges for ε1 [Gt ] ε3. The loss of convergence is because the linear phase of conventional wave-mode functions is ineffective for modelling the modulated phase of the short wave. As expected, this difficulty can be removed by using a modulated wave-mode function for the short wave. On the other hand, for relatively large ε3 ∼O(1), the conventional wave-mode approach converges rapidly while the slowly varying interaction between the two waves cannot be accurately predicted by the present modulated wave-mode approach. These findings have important implications to (time-domain) numerical simulations of the nonlinear evolution of ocean wave fields, and suggest that a hybrid wave model employing both conventional (for large-ε3 interactions) and modulated (for small-ε3 interactions) wave-mode functions should be particularly effective.

scholarly journals Non-Gaussian interaction information: estimation, optimization and diagnostic application of triadic wave resonance

2015 ◽  
Vol 22 (1) ◽  
pp. 87-108 ◽  
Author(s):  
C. A. L. Pires ◽  
R. A. P. Perdigão
Keyword(s):  
Resonance Condition ◽  
Probability Distributions ◽  
Optimization Method ◽  
Statistical Dependence ◽  
Third Order ◽  
Interaction Information ◽  
Wave Resonance ◽  
Wave Trains ◽  
Non Gaussian ◽  
Nonlinear Correlations

Abstract. Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross-cumulants. Its application to a minimal one-dimensional, periodic, advective model leads to enhanced triads that occur between oscillating components of circular or locally confined wave trains satisfying the triadic wave resonance condition.

scholarly journals The Environmental Impact of Transport Activities for Online and In-Store Shopping: A Systematic Literature Review to Identify Relevant Factors for Quantitative Assessments

2021 ◽  
Vol 13 (5) ◽  
pp. 2981
Author(s):  
Susanne Feichtinger ◽  
Manfred Gronalt
Keyword(s):  
Environmental Impact ◽  
Distribution Channel ◽  
Order Effects ◽  
Third Order ◽  
Screening Process ◽  
Environmental Friendliness ◽  
Number Of Factors ◽  
Recommendations For Action ◽  
Behavioural Factors ◽  
Relevant Factors

In the scientific literature, there are numerous studies with different approaches and focuses on assessing the environmental impact of online shopping and shopping in the traditional retail channel. The aim of this work is to analyse scientific studies that quantitatively assess the environmental impact of transport activities in both channels and to extract the factors used for this assessment. A literature search was conducted for the period 2006 to October 2020, with 90 studies shortlisted, of which 15 studies were identified as relevant in a screening process. The analysis showed that a different number of factors is included in the selected studies. Logistics-related and behavioural factors are mostly of similar importance. Third-order effects, such as rebound or complementary effects, are rarely considered. Furthermore, it becomes clear that the results also depend on differences in study design and external factors. This work illustrates the complexity of quantitatively assessing the environmental impact of online and in-store shopping. Caution is advised when deriving recommendations for action from general statements about the environmental friendliness of a distribution channel. The 15 factors found, together with the classification method used, form a solid basis for building new models.

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.

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