A simple model of wave–current interaction

2015 ◽  
Vol 775 ◽  
pp. 328-348 ◽  
Author(s):  
Nicoletta Tambroni ◽  
Paolo Blondeaux ◽  
Giovanna Vittori
Keyword(s):  
Wave Propagation ◽  
Perturbation Approach ◽  
Wave Steepness ◽  
One Dimensional ◽  
Steady Current ◽  
Order Of Magnitude ◽  
Current Interaction ◽  
Viscous Boundary ◽  
The Waves ◽  
Theoretical Results

The interaction between a steady current and propagating surface waves is investigated by means of a perturbation approach, which assumes small values of the wave steepness and considers current velocities of the same order of magnitude as the amplitude of the velocity oscillations induced by wave propagation. The problems, which are obtained at the different orders of approximation, are characterized by a further parameter which is the ratio between the thickness of the bottom boundary layer and the length of the waves and turns out to be even smaller than the wave steepness. However, the solution is determined from the bottom up to the free surface, without the need to split the fluid domain into a core region and viscous boundary layers. Moreover, the procedure, which is employed to solve the problems at the different orders of approximation, reduces them to one-dimensional problems. Therefore, the solution for arbitrary angles between the direction of the steady current and that of wave propagation can be easily obtained. The theoretical results are compared with experimental measurements; the fair agreement found between the model results and the laboratory measurements supports the model findings.

scholarly journals Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 443-452
Author(s):  
Tianshu Jiang ◽  
Anan Fang ◽  
Zhao-Qing Zhang ◽  
Che Ting Chan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Random Media ◽  
Normal Incidence ◽  
Disordered Media ◽  
One Dimensional ◽  
Gain Loss ◽  
The Waves ◽  
Localization Behavior

AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

scholarly journals Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling

2020 ◽  
Vol 221 (3) ◽  
pp. 1580-1590 ◽  
Author(s):  
M van Driel ◽  
C Boehm ◽  
L Krischer ◽  
M Afanasiev
Keyword(s):  
Wave Propagation ◽  
Adaptive Mesh Refinement ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Space ◽  
Adaptive Mesh ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Adjoint Modelling ◽  
The Waves

SUMMARY An order of magnitude speed-up in finite-element modelling of wave propagation can be achieved by adapting the mesh to the anticipated space-dependent complexity and smoothness of the waves. This can be achieved by designing the mesh not only to respect the local wavelengths, but also the propagation direction of the waves depending on the source location, hence by anisotropic adaptive mesh refinement. Discrete gradients with respect to material properties as needed in full waveform inversion can still be computed exactly, but at greatly reduced computational cost. In order to do this, we explicitly distinguish the discretization of the model space from the discretization of the wavefield and derive the necessary expressions to map the discrete gradient into the model space. While the idea is applicable to any wave propagation problem that retains predictable smoothness in the solution, we highlight the idea of this approach with instructive 2-D examples of forward as well as inverse elastic wave propagation. Furthermore, we apply the method to 3-D global seismic wave simulations and demonstrate how meshes can be constructed that take advantage of high-order mappings from the reference coordinates of the finite elements to physical coordinates. Error level and speed-ups are estimated based on convergence tests with 1-D and 3-D models.

Phase shift of solitary wave in a one-dimensional granular chain

2019 ◽  
Vol 33 (10) ◽  
pp. 1950085
Author(s):  
Xian-Qing Yang ◽  
Yao Yang ◽  
Yang Jiao ◽  
Wei Zhang
Keyword(s):  
Phase Shift ◽  
Solitary Wave ◽  
Numerical Scheme ◽  
Binary Collision ◽  
One Dimensional ◽  
Binary Collision Approximation ◽  
Fifth Order ◽  
The Waves ◽  
Theoretical Results ◽  
Collision Approximation

In this paper, both the fifth-order Runge–Kutta numerical scheme and binary collision approximation are used to study the phase shift. Both numerical and theoretical results are shown that the solitary wave after head-on collision propagates along the chain behind the reference wave in both even and odd numbers of grain chains. It is the well-known feature of the appearance of the phase shift. Those results are in agreement with the experimental results. Furthermore, it is found that the phase shift is not only related to the collision position of the waves, but also to the position where the time is measured. The value of phase shift increases nonmonotonously with increasing the velocity of the opposite propagation of the wave. Binary collision approximation is applied to analyze the phase shift, and it is found that theoretical results agree well with numerical results, especially in the case of phase shift in odd chain.

Wave Propagation and Instability in a Circular Semi-Infinite Liquid Jet Harmonically Forced at the Nozzle

1978 ◽  
Vol 45 (3) ◽  
pp. 469-474 ◽  
Author(s):  
D. B. Bogy
Keyword(s):  
Wave Propagation ◽  
Radiation Condition ◽  
Liquid Jet ◽  
Propagation Characteristics ◽  
Frequency Spectra ◽  
One Dimensional ◽  
Wave Numbers ◽  
Complex Wave ◽  
The Stability ◽  
The Waves

The linearized form of the inviscid, one-dimensional Cosserat jet equations derived by Green [6] are used to study wave propagation in a circular jet with surface tension. The frequency spectra are shown for complex wave numbers for a complete range of Weber numbers. The propagation characteristics of the waves are studied in order to determine which branches of the frequency spectra to use in the semi-infinite jet problem with harmonic forcing at the nozzle. Two of the four branches are eliminated by a radiation condition that energy must be outgoing at infinity; the remaining two branches are used to satisfy the nozzle boundary conditions. The variation of the jet radius along its length is shown graphically for various Weber numbers and forcing frequencies. The stability or instability is explained in terms of the behavior of the two propagating phases.

Influence of surface gravity waves on wind-driven circulation in intermediate depths on an exposed coast

1990 ◽  
Vol 41 (3) ◽  
pp. 353 ◽  
Author(s):  
KP Black ◽  
PE McShane
Keyword(s):  
Gravity Waves ◽  
Interaction Theory ◽  
Linear Interaction ◽  
Waves And Currents ◽  
Order Of Magnitude ◽  
Current Interaction ◽  
Wind Driven Currents ◽  
The Waves ◽  
Bed Friction ◽  
Systematic Reduction

Coastal experiments in 18 m depths showed the systematic reduction of wind-driven longshore currents in the presence of surface waves. Predicted wind-driven currents were found to be nearly an order of magnitude greater than measurements if the wave influence was neglected. However, satisfactory predictions were made when the increased effective bed friction due to the non-linear interaction between the waves and currents was accounted for. This paper assesses the applicability of wave/current interaction theory to natural open-coast environments. The results are relevant to the prediction of dispersal (e.g. of pollutants or larvae) on open coasts.

scholarly journals Asymptotic stability of porous-elastic system with thermoelasticity of type III

2021 ◽  
Author(s):  
Ilyes Lacheheb ◽  
Salim A. Messaoudi ◽  
Mostafa Zahri
Keyword(s):  
Wave Propagation ◽  
Asymptotic Stability ◽  
Finite Difference ◽  
Elastic System ◽  
Well Posedness ◽  
One Dimensional ◽  
Type Iii ◽  
The Stability ◽  
Theoretical Results ◽  
Finite Difference Techniques

AbstractIn this work, we investigate a one-dimensional porous-elastic system with thermoelasticity of type III. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. At the end, we use some numerical approximations based on finite difference techniques to validate the theoretical results.

A Perturbation Approach for Predicting Wave Propagation in One-Dimensional Nonlinear Periodic Structures

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Raj K. Narisetti ◽  
Michael J. Leamy ◽  
Massimo Ruzzene
Keyword(s):  
Wave Propagation ◽  
Numerical Simulations ◽  
Perturbation Analysis ◽  
Periodic Structures ◽  
Harmonic Wave ◽  
Dispersion Relations ◽  
Perturbation Approach ◽  
One Dimensional ◽  
Chain Unit ◽  
Unit Cells

Wave propagation in one-dimensional nonlinear periodic structures is investigated through a novel perturbation analysis and accompanying numerical simulations. Several chain unit cells are considered featuring a sequence of masses connected by linear and cubic springs. Approximate closed-form, first-order dispersion relations capture the effect of nonlinearities on harmonic wave propagation. These relationships document amplitude-dependent behavior to include tunable dispersion curves and cutoff frequencies, which shift with wave amplitude. Numerical simulations verify the dispersion relations obtained from the perturbation analysis. The simulation of an infinite domain is accomplished by employing viscous-based perfectly matched layers appended to the chain ends. Numerically estimated wavenumbers show good agreement with the perturbation predictions. Several example chain unit cells demonstrate the manner in which nonlinearities in periodic systems may be exploited to achieve amplitude-dependent dispersion properties for the design of tunable acoustic devices.

Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yaroslava E. Poroshyna ◽  
Aleksander I. Lopato ◽  
Pavel S. Utkin
Keyword(s):  
Wave Propagation ◽  
Detonation Wave ◽  
Model Comparison ◽  
Approximation Order ◽  
Transition Regime ◽  
Stage Model ◽  
Two Stage ◽  
One Dimensional ◽  
Kinetics Of ◽  
Detonation Wave Propagation

Abstract The paper contributes to the clarification of the mechanism of one-dimensional pulsating detonation wave propagation for the transition regime with two-scale pulsations. For this purpose, a novel numerical algorithm has been developed for the numerical investigation of the gaseous pulsating detonation wave using the two-stage model of kinetics of chemical reactions in the shock-attached frame. The influence of grid resolution, approximation order and the type of rear boundary conditions on the solution has been studied for four main regimes of detonation wave propagation for this model. Comparison of dynamics of pulsations with results of other authors has been carried out.

scholarly journals Universally bistable shells with nonzero Gaussian curvature for two-way transition waves

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nikolaos Vasios ◽  
Bolei Deng ◽  
Benjamin Gorissen ◽  
Katia Bertoldi
Keyword(s):  
Gaussian Curvature ◽  
Energy Landscape ◽  
Propagation Distance ◽  
Energy Landscapes ◽  
Bending Energy ◽  
Nonlinear Dynamic Response ◽  
One Dimensional ◽  
Doubly Curved Shells ◽  
Doubly Curved ◽  
The Waves

AbstractMulti-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.

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