scholarly journals Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 105 ◽  
Author(s):  
James N. Steer ◽  
Mark L. McAllister ◽  
Alistair G. L. Borthwick ◽  
Ton S. van den Bremer
Keyword(s):  
Wave Equation ◽  
Modulational Instability ◽  
Experimental Measurements ◽  
Extreme Waves ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Numerical Predictions ◽  
Wave Basin ◽  
Time Marching ◽  
Modulational Stability

The coupled nonlinear Schrödinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schrödinger wave equation, is characterized (to first order) by an exponential growth of sideband components and the formation of distinct wave pulses, often containing extreme waves. Linear stability analysis of the CNLSE shows the effect of crossing angle, θ , on MI, and reveals instabilities between 0 ∘ < θ < 35 ∘ , 46 ∘ < θ < 143 ∘ , and 145 ∘ < θ < 180 ∘ . Herein, the modulational stability of crossing wavetrains seeded with symmetrical sidebands is determined experimentally from tests in a circular wave basin. Experiments were carried out at 12 crossing angles between 0 ∘ ≤ θ ≤ 88 ∘ , and strong unidirectional sideband growth was observed. This growth reduced significantly at angles beyond θ ≈ 20 ∘ , reaching complete stability at θ = 30–40 ∘ . We find satisfactory agreement between numerical predictions (using a time-marching CNLSE solver) and experimental measurements for all crossing angles.

Relativistic generalization of whistler mode modulational instability

1981 ◽  
Vol 59 (10) ◽  
pp. 1376-1379
Author(s):  
R. Prasad ◽  
G. P. Gupta ◽  
R. N. Singh
Keyword(s):  
Growth Rate ◽  
Wave Equation ◽  
Frequency Spectrum ◽  
Modulational Instability ◽  
Relativistic Plasma ◽  
Relativistic Generalization ◽  
Whistler Mode ◽  
Nonlinear Schrödinger ◽  
Whistler Mode Waves ◽  
Relativistic Particles

The modulational instability of whistler mode waves interacting with relativistic plasma has been studied. The application of the Karpman and Krushkal criterion to the nonlinear Schrödinger wave equation gives the spectrum of modulationally unstable whistler mode waves. The effect of relativistic particles on the growth rate and frequency spectrum of modulationally unstable whistler mode waves has been discussed.

An Appraisal of the Paper by O'Carrol et al. (1990)

1995 ◽  
Vol 209 (3) ◽  
pp. 203-205 ◽  
Author(s):  
A Strozzi ◽  
A Unsworth
Keyword(s):  
Finite Element ◽  
Finite Elasticity ◽  
Experimental Measurements ◽  
Linear Elastic ◽  
Numerical Predictions ◽  
Elasticity Effects

The paper by O'Carrol et al. (1), which addresses the problem of an elastomeric disc indented by a spherical punch, has been evaluated. The sources of disagreement between linear elastic numerical predictions and experimental measurements noted in this paper have been critically examined in the light of finite element forecasts obtained with a package which incorporates finite elasticity effects and incompressibility.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

Application of unsplit convolutional perfectly matched layer for scalar arbitrarily wide-angle wave equation

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. T313-T321 ◽  
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
Yanqi Li
Keyword(s):  
Wave Equation ◽  
Computational Cost ◽  
Grazing Incidence ◽  
Equation System ◽  
Perfectly Matched Layer ◽  
Staggered Grid ◽  
Complex Frequency ◽  
Wide Angle ◽  
First Order ◽  
General Complex

A classical split perfectly matched layer (PML) method has recently been applied to the scalar arbitrarily wide-angle wave equation (AWWE) in terms of displacement. However, the classical split PML obviously increases computational cost and cannot efficiently absorb waves propagating into the absorbing layer at grazing incidence. Our goal was to improve the computational efficiency of AWWE and to enhance the suppression of edge reflections by applying a convolutional PML (CPML). We reformulated the original AWWE as a first-order formulation and incorporated the CPML with a general complex frequency shifted stretching operator into the renewed formulation. A staggered-grid finite-difference (FD) method was adopted to discretize the first-order equation system. For wavefield depth continuation, the first-order AWWE with the CPML saved memory compared with the original second-order AWWE with the conventional split PML. With the help of numerical examples, we verified the correctness of the staggered-grid FD method and concluded that the CPML can efficiently absorb evanescent and propagating waves.

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