scholarly journals Modulational Interactions of Two Monochromatic Waves and Packets of Random Waves

1994 ◽  
Vol 47 (4) ◽  
pp. 375 ◽  
Author(s):  
SV Vladimirov ◽  
SI Popel
Keyword(s):  
Modulational Instability ◽  
Single Mode ◽  
Maximum Effect ◽  
Random Wave ◽  
Random Waves ◽  
Third Order ◽  
Langmuir Waves ◽  
Coupled Equations ◽  
Instability Development ◽  
Field Correlation

The modulational instability of Langmuir waves in unmagnetised plasmas is reviewed for the cases when a pump consist of two monochromatic or a large number of random modes. It is demonstrated that the correct theory for the modulational instability operates with 'renormalised' equations for the linear dielectric function as well as for the effective third-order plasma response. This renormalisation is due to so-called interference terms. The appearance of interference terms is a specific feature of the multi-mode modulational instability in comparison with the well-known instability of a single mode. All calculations use a simple and universal formalism including new methods developed for description of the modulational effects in arbitrary media. The modulational instability of two pump Langmuir modes is considered for the case of comparatively small instability rates, when 'renormalised' expressions for linear and nonlinear plasma polarisation responses provide the maximum effect on the instability development. For instabilities of the broad spectra of random waves, the integral equations are presented for perturbations of wave field correlation functions. In the description of the modulational instability of random wave packets these equations play the same role as the set of coupled equations for the fields of modulational perturbations in the case of two monochromatic pumps. Rates and thresholds of the instabilities are found in various limits.

Theory of modulational interaction of two coupled waves. Part 1. General formulae for a nonlinear medium

1993 ◽  
Vol 49 (2) ◽  
pp. 197-205 ◽  
Author(s):  
Sergey V. Vladimirov ◽  
Vadim N. Tsytovich
Keyword(s):  
Dielectric Function ◽  
Nonlinear Medium ◽  
Modulational Instability ◽  
Single Mode ◽  
Third Order ◽  
Modulational Interaction

The modulational interaction of two waves propagating in a cubically nonlinear medium is considered. It is shown that the correct theory operates with ‘renormalized’ equations for the linear dielectric function and for an effective third-order medium response. This renormalization is due to so-called interference terms. The appearance of interference terms is a specific feature of the two-mode modulational instability in comparison with the well-known instability of a single mode.

Parametric decay of wide band Langmuir wave spectra

2016 ◽  
Vol 82 (6) ◽  
Author(s):  
Mitsuo Kono ◽  
Hans L. Pécseli
Keyword(s):  
Continuous Wave ◽  
Modulational Instability ◽  
Wave Spectrum ◽  
Langmuir Wave ◽  
Single Mode ◽  
Wide Band ◽  
Wave Spectra ◽  
Langmuir Waves ◽  
Parametric Decay ◽  
Wave Models

Previous results obtained for modulational instability of a Langmuir wave spectrum are extended to account also for the Langmuir wave decay. The general model is tested by considering first the parametric decay of single-mode Langmuir waves, and also two-wave models, where several combinations are considered: one wave is modulationally unstable, another decay unstable and one where both waves are unstable with respect to decay. For the general case with continuous wave spectra it is found that distribution of the Langmuir wave energy over a wide wavenumber band reduces the decay rate when the correlation length for the spectrum becomes comparable to the wavelength of the most unstable sound wave among the possible decay products.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

Optical bistable switching in pyran dye-doped polymers

2014 ◽  
Vol 23 (02) ◽  
pp. 1450018 ◽  
Author(s):  
Purnima ◽  
Devendra Mohan
Keyword(s):  
Solid State ◽  
Communication Systems ◽  
Optical Bistability ◽  
Nonlinear Refraction ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Third Order ◽  
Bistable Switching ◽  
Fabry Perot ◽  
Doped Polymers

In the present frame of work, optical bistability using a Fabry–Perot (FP) cavity containing 4-dicyanomethylene-2-methyl-6-p-dimethylaminostyryl-4H-pyran (DCM) dye entrapped in poly-methylmethacrylate (PMMA) matrix is experimentally investigated. Optical nonlinear behavior of solid-state samples is studied using a single-mode Q-switched nanosecond Nd:YAG laser operating at 532 nm. Various optical nonlinear parameters such as nonlinear refractive index (n2) and third-order susceptibility (χ3) of the material are numerically estimated from bistability loops. The origin of optically bistable behavior is attributed to photoisomerization-assisted nonlinear refraction phenomenon. It is observed that nonlinear refraction dominates over nonlinear absorption in giving rise to the optical bistability. The study shows that DCM dye entrapped in solid-state matrices are promising candidate for polymer-based optical switches, data processing, and communication systems.

Experimental Study of Slow-Drift Ship Motions in Shallow Water Random Waves

2011 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Trygve Kristiansen
Keyword(s):  
Spectral Analysis ◽  
Shallow Water ◽  
Transfer Functions ◽  
Second Order ◽  
Ship Motions ◽  
Random Wave ◽  
Random Waves ◽  
Low Frequencies ◽  
Wave Basin ◽  
Drift Forces

Slowly varying motions and drift forces of a large moored ship in random waves at 35m water depth are investigated by an experimental wave basin study in scale 1:50. A simple horizontal mooring set-up is used. A second-order wave correction is applied to minimize “parasitic” long waves. The effect on the ship motion from the correction is clearly seen, although less in random wave spectra than in pure bi-chromatic waves. Empirical quadratic transfer functions (QTFs) of the surge drift force are found by use of cross-bi-spectral analysis, in two different spectra have been obtained. The QTF levels increase significantly with lower wave frequencies (except at the diagonal), which is special for finite and shallow water. Furthermore, the QTF levels frequencies at low frequencies increase significantly out from the QTF diagonal. Thus Newman’s approximation should preferrably not be used in these cases. Using the LF waves as a direct excitation in a “linear” ship force analysis gives random records that compare reasonably well with those from the cross-bi-spectral analysis. This confirms the idea that the drift forces in shallow water are closely correlated to the second-order potential, and thereby by the second-order LF waves.

scholarly journals Comparison of Extreme Surface Elevation for Linear and Nonlinear Random Wave Theory for Offshore Structures

2018 ◽  
Vol 203 ◽  
pp. 01021
Author(s):  
Nurul 'Azizah Mukhlas ◽  
Noor Irza Mohd Zaki ◽  
Mohd Khairi Abu Husain ◽  
Gholamhossein Najafian
Keyword(s):  
Probabilistic Approach ◽  
Wave Theory ◽  
Offshore Structures ◽  
Random Wave ◽  
Linear Wave ◽  
Random Waves ◽  
Sea State ◽  
Higher Order Terms ◽  
Structural Responses ◽  
Nonlinear Random Wave

For offshore structural design, the load due to wind-generated random waves is usually the most important source of loading. While these structures can be designed by exposing them to extreme regular waves (100-year design wave), it is much more satisfactory to use a probabilistic approach to account for the inherent randomness of the wave loading. This method allows the statistical properties of the loads and structural responses to be determined, which is essential for the risk-based assessment of these structures. It has been recognized that the simplest wave generation is by using linear random wave theory. However, there is some limitation on its application as some of the nonlinearities cannot be explained when higher order terms are excluded and lead to underestimating of 100-year wave height. In this paper, the contribution of nonlinearities based on the second order wave theory was considered and being tested at a variety of sea state condition from low, moderate to high. Hence, it was proven that the contribution of nonlinearities gives significant impact the prediction of 100-year wave's design as it provides a higher prediction compared to linear wave theory.

scholarly journals Nonlinear spectral model for rotating sheared turbulence

2019 ◽  
Vol 866 ◽  
pp. 5-32 ◽  
Author(s):  
Ying Zhu ◽  
C. Cambon ◽  
F. S. Godeferd ◽  
A. Salhi
Keyword(s):  
Turbulent Shear ◽  
Finite Difference Schemes ◽  
Turbulent Shear Flow ◽  
Third Order ◽  
Mean Velocity ◽  
Coupled Equations ◽  
Velocity Gradients ◽  
Model Predictions ◽  
Pseudo Scalar ◽  
High Order Finite Difference

We propose a statistical model for homogeneous turbulence undergoing distortions, which improves and extends the MCS model by Mons, Cambon & Sagaut (J. Fluid Mech., vol. 788, 2016, 147–182). The spectral tensor of two-point second-order velocity correlations is predicted in the presence of arbitrary mean-velocity gradients and in a rotating frame. For this, we numerically solve coupled equations for the angle-dependent energy spectrum${\mathcal{E}}(\boldsymbol{k},t)$that includes directional anisotropy, and for the deviatoric pseudo-scalar $Z(\boldsymbol{k},t)$, that underlies polarization anisotropy ($\boldsymbol{k}$ is the wavevector,$t$the time). These equations include two parts: (i) exact linear terms representing the viscous spectral linear theory (SLT) when considered alone; (ii) generalized transfer terms mediated by two-point third-order correlations. In contrast with MCS, our model retains the complete angular dependence of the linear terms, whereas the nonlinear transfer terms are closed by a reduced anisotropic eddy damped quasi-normal Markovian (EDQNM) technique similar to MCS, based on truncated angular harmonics expansions. And in contrast with most spectral approaches based on characteristic methods to represent mean-velocity gradient terms, we use high-order finite-difference schemes (FDSs). The resulting model is applied to homogeneous rotating turbulent shear flow with several Coriolis parameters and constant mean shear rate. First, we assess the validity of the model in the linear limit. We observe satisfactory agreement with existing numerical SLT results and with theoretical results for flows without rotation. Second, fully nonlinear results are obtained, which compare well to existing direct numerical simulation (DNS) results. In both regimes, the new model improves significantly the MCS model predictions. However, in the non-rotating shear case, the expected exponential growth of turbulent kinetic energy is found only with a hybrid model for nonlinear terms combining the anisotropic EDQNM closure and Weinstock’s return-to-isotropy model.

The Diffraction of Multidirectional Random Waves by Trapezoidal Submarine Pits

2003 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams ◽  
Sung Duk Kim
Keyword(s):  
Numerical Model ◽  
Wave Diffraction ◽  
Boundary Integral ◽  
Random Wave ◽  
Linear Wave ◽  
Wave System ◽  
Random Waves ◽  
Random Surface ◽  
Directional Spectrum ◽  
Integral Equation Approach

A numerical model is presented to predict the interaction of multidirectional random surface waves with one or more trapezoidal submarine pits. In the present formulation, each pit may have a different side slope, while the four side slopes at the interior edge of any given pit are assumed equal. The water depth in the fluid region exterior to the pits is taken to be uniform, and the solution method for a random wave system involves the superposition of linear-wave diffraction solutions based on a two-dimensional boundary integral equation approach. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The results of the present numerical model have been compared with those of previous theoretical studies for regular and random wave diffraction by single or multiple rectangular pits. Reasonable agreement was obtained in all cases. Based on these comparisons it is concluded that the present numerical model is an accurate and efficient tool to predict the wave field around multiple submarine pits of trapezoidal section in many practical situations.

scholarly journals Random wave-driven drag forces on near-bed vegetation in shallow water based on deepwater wind conditions

2019 ◽  
Vol 233 (4) ◽  
pp. 1287-1290
Author(s):  
Dag Myrhaug
Keyword(s):  
Shallow Water ◽  
Drag Force ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Random Wave ◽  
Random Waves ◽  
Coastal Zones ◽  
Drag Forces ◽  
Mean Wind Speed ◽  
Wave Induced

This article provides a simple analytical method for giving estimates of random wave-driven drag forces on near-bed vegetation in shallow water from deepwater wind conditions. Results are exemplified using a Pierson–Moskowitz model wave spectrum for wind waves with the mean wind speed at the 10 m elevation above the sea surface as the parameter. The significant value of the drag force within a sea state of random waves is given, and an example typical for field conditions is presented. This method should serve as a useful tool for assessing random wave-induced drag force on vegetation in coastal zones and estuaries based on input from deepwater wind conditions.

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