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.

A stochastic model of sea-surface roughness. I. Wave crests

1987 ◽  
Vol 410 (1838) ◽  
pp. 19-34 ◽  
Keyword(s):  
Surface Roughness ◽  
Random Noise ◽  
Wave Spectrum ◽  
Short Wave ◽  
Sea Surface ◽  
Scale Model ◽  
Wave Steepness ◽  
Wave Interactions ◽  
Long Wave ◽  
Sea Surface Roughness

In this paper we develop a two-scale model of sea-surface roughness, in which for the first time the randomness of both long and short waves is taken fully into account. The model includes long–wave-short-wave interactions, dissipation of the short-wave energy by breaking, and regeneration by the wind. This leads to an integral equation for the short-wave steepness, which is solved by iteration. The effects of wind speed and of long-wave steepness upon the distribution of roughness at the long-wave crests are calculated and discussed. Also the effect of a band-width parameter for the long-wave spectrum. A random noise source can be included.

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 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.

Phase velocity effects in tertiary wave interactions

1962 ◽  
Vol 12 (3) ◽  
pp. 333-336 ◽  
Author(s):  
M. S. Longuet-Higgins ◽  
O. M. Phillips
Keyword(s):  
Phase Velocity ◽  
Continuous Spectrum ◽  
Deep Water ◽  
Wave Train ◽  
The Other ◽  
Wave Number ◽  
Wave Interactions ◽  
Single Wave ◽  
Phase Velocities ◽  
Wave Trains

It is shown that, when two trains of waves in deep water interact, the phase velocity of each is modified by the presence of the other. The change in phase velocity is of second order and is distinct from the increase predicted by Stokes for a single wave train. When the wave trains are moving in the same direction, the increase in velocity Δc2 of the wave with amplitude a2, wave-number k2 and frequency α2 resulting from the interaction with the wave (a1, k1, σ1) is given by Δc2 = a21k1σ1, provided k1 < k2. If k1 > k2, then Δc2 is given by the same expression multiplied by k2/k1. If the directions of propagation are opposed, the phase velocities are decreased by the same amount. These expressions are extended to give the increase (or decrease) in velocity due to a continuous spectrum of waves all travelling in the same (or opposite) direction.

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.

Near-Infrared Combination and Overtone Bands of CH in CHX3, CHX2—CHX2, and CHX2—CX2—CHX2

2005 ◽  
Vol 59 (11) ◽  
pp. 1393-1398 ◽  
Author(s):  
Reikichi Iwamoto ◽  
Akishi Nara ◽  
Toshihiko Matsuda
Keyword(s):  
Excited State ◽  
Near Infrared ◽  
Present Report ◽  
Spectral Characteristics ◽  
The Other ◽  
Coupled Modes ◽  
Third Order ◽  
The Third ◽  
Combination Bands ◽  
Deformation Modes

In the present report we studied spectral characteristics of the near-infrared combination and overtone bands of CH vibrations of a CH sequence. The near-infrared bands of the CH in CHX3 (X, halogen), which were interpreted in terms of the CH stretching and CH deformation fundamentals without any ambiguity, typically showed how the frequency and intensity of a combination or an overtone depend on the vibrational excited state. In the CH–C–CH of CHX2CX2CHX2, the vibrations of one CH are isolated from those of the other CH, and the combination and overtone bands were similarly interpreted as those of the CH, although each of the combination bands was split into two because of non-degeneracy of the CH deformation. In the CH–CH of CHX2CHX2, the CH deformations only have coupled modes. The first combination showed four narrowly separate bands, which were reasonably interpreted on the basis of the CH stretching and the coupled CH deformation modes. We demonstrated that the first combination of coupled modes as well as the combination of up to, at least, the third order of isolated modes have the nature of the characteristic bands.

NUMERICAL ANALYSIS OF LASER DIODE LONGITUDINALLY PUMPED SOLID‐STATE LASER GENERATION DYNAMICS USING TRAVELING WAVE MODEL

2010 ◽  
Vol 15 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Aleksandr Dementjev ◽  
Raimondas Čiegis ◽  
Ingrida Laukaitytė ◽  
Nerijus Slavinskis
Keyword(s):  
Solid State ◽  
Traveling Wave ◽  
Wave Model ◽  
Solid State Laser ◽  
The Other ◽  
Laser Generation ◽  
Solid State Lasers ◽  
Q Switching ◽  
Laser Pulse Intensity ◽  
Laser Model

A detailed theoretical model for the description of generation dynamics of diode laser longitudinally pumped solid‐state lasers with active and/or passive Q‐switching using traveling wave approach is presented. The results of numerical simulations and analysis show that the distribution of generated laser pulse intensity and the other laser parameters along the resonator is very inhomogeneous. Therefore, the widely used point laser model cannot give accurate results when inside the resonator there are active or passive elements which lead to the strong modulation of the generated pulse intensities.

scholarly journals Method of obtaining and studying the optical properties of carbon quantum dots.

2019 ◽  
Vol 19 (3) ◽  
pp. 226-229
Author(s):  
S.D. Bardasevska ◽  
I.M. Budzulyak ◽  
S.I. Budzulyak ◽  
B.I. Rachiy ◽  
R.V. Ilnytskyi ◽  
...  
Keyword(s):  
Raw Materials ◽  
Wavelength Region ◽  
Short Wave ◽  
Carbon Quantum Dots ◽  
Long Wavelength ◽  
Plant Raw Materials ◽  
Wave Region ◽  
Exciton Mechanism ◽  
Short Wave Region ◽  
Kinetics Of

The proposed method of synthesis of CQDs on the basis of nanoporous carbon obtained from plant raw materials. It is established that in the short-wave region a band is registered, which is due to the exciton mechanism of recombination, whereas in the long-wavelength region it is related to the state of defects. The kinetics of PL extinction is not strictly exponential, which most likely indicates the distributed nature of fading from individual emitters.

The United States and Iran

2018 ◽  
Author(s):  
Ray Takeyh
Keyword(s):  
United States ◽  
National Security ◽  
Decision Maker ◽  
The United States ◽  
The Other ◽  
Order Effects ◽  
Optimal Outcome ◽  
Third Order ◽  
National Interests ◽  
Taking Action

Implementing deterrent and compellent strategies are among the most critical tasks of the national security decision maker. However, as the case of U.S.-Iranian relations since 1979 demonstrates, deterring another state from taking action—especially if it considers those steps to be in its national interests—or compelling it to adopt policies in line with one’s own preferences but which represent a setback to the goals of the other state can be a difficult proposition. In addition, the Iran relationship demonstrates howthe use of deterrent and compellent instruments must be weighed against costs and other second- and third-order effects which may cause the policymaker to accept a less than optimal outcome in order to avoid greater complications in other areas.

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