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 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)’.

scholarly journals Nonlinear long waves over a muddy beach

2013 ◽  
Vol 718 ◽  
pp. 371-397 ◽  
Author(s):  
Erell-Isis Garnier ◽  
Zhenhua Huang ◽  
Chiang C. Mei
Keyword(s):  
Boundary Layer ◽  
Thin Layer ◽  
Surface Waves ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Long Waves ◽  
Fluid Mud ◽  
Weakly Nonlinear ◽  
Sea Bottom ◽  
Oscillatory Boundary Layer

AbstractWe analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.

Surface Oscillations of Water in a Rotating Cylindrical Vessel

1930 ◽  
Vol 26 (4) ◽  
pp. 446-452 ◽  
Author(s):  
R. O. Street
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Cross Section ◽  
Circular Cross Section ◽  
Cylindrical Vessel ◽  
Long Waves ◽  
Horizontal Velocity ◽  
Uniform Rotation ◽  
Tidal Waves ◽  
Short Waves

This paper is devoted chiefly to the consideration of the surface oscillations of water contained in a vessel in the shape of a circular cylinder with its axis vertical, when the motion is slightly disturbed from a uniform rotation about the axis of the vessel. The work was undertaken with the hope of finding some indication of the effect of the depth of the water in the vessel on the period of the surface waves, and for the purpose a vessel of circular cross-section was naturally chosen. It is shown that a slight change of shape does not affect the periods of the oscillations. The solution of the corresponding problem when the surface oscillations take the form of “long waves” or “tidal waves” is well known, and the present paper deals only with “short waves,” for which the horizontal velocity is not the same at all depths.

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.

A nonlinear mechanism for the generation of sea waves

1969 ◽  
Vol 311 (1506) ◽  
pp. 371-389 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Waves ◽  
Orbital Motion ◽  
Long Waves ◽  
Shear Instability ◽  
Sea Waves ◽  
Short Waves ◽  
Long Wave ◽  
Nonlinear Mechanism ◽  
Surrounding Fluid

Recent observations of the growth of sea waves under the action of wind have established that the rate of growth is several times greater than has yet been accounted for. In this paper a new mechanism of wave generation is proposed, based on the idea of a maser-like action of the short waves on the longer waves. It is shown that when surface waves decay they impart their momentum to the surrounding fluid. Short waves are readily regenerated by shear instability. But a longer wave passing through shorter waves causes the short waves to steepen on the long-wave crests. Hence the short waves impart more of their momentum to the crests of the long waves, where the orbital motion of the long waves is in the direction of wave propagation. If the short waves are decaying only weakly (under the action of viscosity), the effect on the long waves is slight. But when the short waves are forced to decay strongly by breaking on the forward slopes of the long waves the gain of energy by the latter is greatly increased. Calculations suggest that the mechanism is capable of imparting energy to sea waves at the rate observed.

The generation of surface waves over a sloping beach by an oscillating line source

1976 ◽  
Vol 79 (3) ◽  
pp. 573-585 ◽  
Author(s):  
Clare A. N. Morris
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Line Source ◽  
Short Wave ◽  
Long Waves ◽  
Edge Waves ◽  
Wave Regime ◽  
Wave Solutions ◽  
Sloping Beach

AbstractA line source whose strength varies sinusoidally with time and also with the co-ordinate measured along its length is situated parallel to the shoreline of a beach of angle ¼π0. Both long-and short-wave solutions are found. It is shown that for certain positions of the source, long waves are not radiated to infinity, while in the short-wave regime, the solutions take the form of edge-waves, with resonances occurring at certain wavenumbers. Computations of the free-surface contours are presented for a range of wavenumbers.

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.

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
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