scholarly journals Experimental Dispersion Relation of Surface Waves along a Torus of Fluid

2021 ◽  
Vol 127 (14) ◽  
Author(s):  
Filip Novkoski ◽  
Eric Falcon ◽  
Chi-Tuong Pham
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Experimental Dispersion

scholarly journals Frequency-dependent impedance and surface waves on the boundary of a stratified dielectric medium

2019 ◽  
Vol 377 (2156) ◽  
pp. 20190218
Author(s):  
Kirill Cherednichenko ◽  
William Graham
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Half Space ◽  
Dielectric Medium ◽  
Interface Condition ◽  
Theme Issue ◽  
Structured Media ◽  
Loss Parameter ◽  
The Relationship ◽  
Dynamic Phenomena

We analyse waves propagating along the interface between half-spaces filled with a perfect dielectric and a Lorentz material. We show that the corresponding interface condition leads to a generalization of the classical Leontovich condition on the boundary of a dielectric half-space. We study when this condition supports propagation of (dispersive) surface waves. We derive the related dispersion relation for waves along the boundary of a stratified half-space and determine the relationship between the loss parameter, frequency and wavenumber for which interfacial waves exist. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

Envelope solitons of surface waves in a plasma column

1987 ◽  
Vol 38 (3) ◽  
pp. 427-437 ◽  
Author(s):  
D. Grozev ◽  
A. Shivarova ◽  
A. D. Boardman
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Plasma Column ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Nonlinear Dispersion ◽  
Dark Solitons ◽  
Envelope Solitons ◽  
Nonlinear Dispersion Relation ◽  
Universal Procedure

The problem of envelope solitons of surface waves is considered on the basis of results for the nonlinear dispersion relation of the waves in a plasma column. The soliton solutions are derived as particular cases of the general solutions obtained by a universal procedure and expressed in terms of Jacobi elliptic functions. Since the two types of interactions, namely the (ω + ω) – ω and the (ω – ω) + ω interactions (where ω is the frequency of the carrier wave) included in the nonlinear dispersion relation act in opposite ways, existence both of bright and dark solitons is shown to be possible. The effect of the ponderomotive force that in our case is expressed through the contribution of the (ω – ω) + ω interaction leads to the formation of dark solitons. The effect of the losses is also considered.

Finite-frequency surface waves on current sheets

1991 ◽  
Vol 45 (3) ◽  
pp. 389-406 ◽  
Author(s):  
K. P. Wessen ◽  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Cyclotron Frequency ◽  
Low Frequency ◽  
Dielectric Tensor ◽  
Magnetic Field Direction ◽  
Field Reversal ◽  
Ion Cyclotron ◽  
The Magnetic Field

The dispersion relation for low-frequency surface waves at a current sheet between two magnetized plasmas is derived using the cold-plasma dielectric tensor with finite ion-cyclotron frequency. The magnetic field direction is allowed to change discontinuously across the sheet, but the plasma density remains constant. The cyclotron frequency causes a splitting of the dispersion relation into a number of mode branches with frequencies both less than and greater than the ion-cyclotron frequency. The existence of these modes depends in particular upon the degree of magnetic field discontinuity and the direction of wave propagation in the sheet relative to the magnetic field directions. Sometimes two modes can exist for the same direction of propagation. The existence of modes undamped by Alfvén resonance absorption is predicted. Analytical solutions are obtained in the low-frequency and magnetic-field-reversal limits. The solutions are obtained numerically in the general case.

scholarly journals Faraday waves: their dispersion relation, nature of bifurcation and wavenumber selection revisited

2015 ◽  
Vol 777 ◽  
Author(s):  
Jean Rajchenbach ◽  
Didier Clamond
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Significant Role ◽  
Current Literature ◽  
Theoretical Description ◽  
Long Waves ◽  
Faraday Waves ◽  
Wavenumber Selection

In the current literature, the dispersion relation of parametrically forced surface waves is often identified with that of free unforced waves. We revisit here the theoretical description of Faraday waves, showing that forcing and dissipation play a significant role in the dispersion relation, rendering it bi-valued. We then determine the instability thresholds and the wavenumber selection in cases of both short and long waves. We show that the bifurcation can be either supercritical or subcritical, depending on the depth.

scholarly journals Waves’ Numerical Dispersion and Damping due to Discrete Dispersion Relation

2014 ◽  
Author(s):  
Babak Ommani ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Boundary Integral ◽  
Panel Method ◽  
Numerical Dispersion ◽  
Finite Difference Schemes ◽  
Rankine Panel Method ◽  
Free Surface Waves ◽  
The Waves

In linear Rankine panel method, the discrete linear dispersion relation is solved on a discrete free-surface to capture the free-surface waves generated due to wave-body interactions. Discretization introduces numerical damping and dispersion, which depend on the discretization order and the chosen methods for differentiation in time and space. The numerical properties of a linear Rankine panel method, based on a direct boundary integral formulation, for capturing two and three dimensional free-surface waves were studied. Different discretization orders and differentiation methods were considered, focusing on the linear distribution and finite difference schemes. The possible sources for numerical instabilities were addressed. A series of cases with and without forward speed was selected, and numerical investigations are presented. For the waves in three dimensions, the influence of the panels’ aspect ratio and the waves’ angle were considered. It has been shown that using the cancellation effects of different differentiation schemes the accuracy of the numerical method could be improved.

Comment on ‘Boundary conditions for surface waves propagating along the interface of plasma flow and free space’

1999 ◽  
Vol 61 (1) ◽  
pp. 169-171 ◽  
Author(s):  
MAGDI SHOUCRI
Keyword(s):  
Dispersion Relation ◽  
Boundary Conditions ◽  
Surface Waves ◽  
Plasma Flow ◽  
Free Space ◽  
Plasma Phys ◽  
Plane Interface

The dispersion relation and boundary conditions for surface waves propagating on the plane interface between a vacuum and a drifting plasma have recently been derived by Lee and Cho [J. Plasma Phys.58, 409 (1997)]. It is the purpose of the present comment to show that the boundary conditions and dispersion relation are incorrect.

scholarly journals A new misfit function for multimodal inversion of surface waves

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. G31-G43 ◽  
Author(s):  
Margherita Maraschini ◽  
Fabian Ernst ◽  
Sebastiano Foti ◽  
Laura Valentina Socco
Keyword(s):  
Surface Waves ◽  
Dispersion Curve ◽  
A Priori ◽  
Model Resolution ◽  
Higher Modes ◽  
Modal Dispersion ◽  
Velocity Models ◽  
Wave Inversion ◽  
Data Points ◽  
Experimental Dispersion

Higher-mode contribution is important in surface-wave inversion because it allows more information to be exploited, increases investigation depth, and improves model resolution. A new misfit function for multimodal inversion of surface waves, based on the Haskell-Thomson matrix method, allows higher modes to be taken into account without the need to associate experimental data points to a specific mode, thus avoiding mode-misidentification errors in the retrieved velocity profiles. Computing cost is reduced by avoiding the need for calculating synthetic apparent or modal dispersion curves. Based on several synthetic and real examples with inversion results from the classical and the proposed methods, we find that correct velocity models can be retrieved through the multimodal inversion when higher modes are superimposed in the apparent dispersion-curve or when it is not trivial to determine a priori to which mode each data point of the experimental dispersion curve belongs. The main drawback of the method is related to the presence of several local minima in the misfit function. This feature makes the choice of a consistent initial model very important.

Surface waves on the spin-1/2 quantum magnetoplasma half-space

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
Jun Zhu
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Half Space ◽  
Electron Spin ◽  
Electron Plasma ◽  
Degenerate Electron ◽  
Spin Effects ◽  
Bohm Potential ◽  
Magnetohydrodynamic Model ◽  
Plasmon Polaritons

We present a theoretical investigation on the propagation of surface waves on the magnetized degenerate electron plasma half-space with spin effects. Using magnetohydrodynamic model with quantum effects due to the Bohm potential, Fermi degenerate pressure and electron spin, the dispersion relations of surface plasmon polaritons (SPPs) are derived. The dispersion relation of electrostatic surface waves is also obtained by taking electrostatic limit.

The Square Root Approximation to the Dispersion Relation of the Axially-symmetric Electron Wave on a Cylindrical Plasma

1997 ◽  
Vol 52 (10) ◽  
pp. 709-712
Author(s):  
V.M. Babović ◽  
B.A. Aničin ◽  
D. M. Davidović
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Gravity Waves ◽  
Water Surface ◽  
Bessel Functions ◽  
Exact Expression ◽  
Square Root ◽  
Axially Symmetric ◽  
Electron Wave ◽  
Surface Gravity Waves

Abstract This paper suggests the use of a simple square root approximation to the dispersion relation of axially-symmetric electron surface waves on cylindrical plasmas. The point is not merely to substitute the exact expression for the dispersion relation which involves a number of Bessel functions with a more tractable analytical approximant, but to cast the dispersion relation in a form useful in the comparison with other waves, such as water surface gravity waves and the associated tide-rip effect. The square root form of the dispersion relation is also of help in the analysis of surfactron plasmas, as it directly predicts a linear roll-off of electron density in the discharge.

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