Damping Of Surface Waves Research Articles

The Saddle-Point Approximation for Damped Surface Waves

Summary A result due to Brune on the damping of surface waves is proved in rather more detail.

On the interaction of adjacent hot plasma streams. I. Dielectric permeability tensor components

The expressions for the components of the dielectric permeability tensor of a relativistic plasma stream have been obtained. The parameters (density, longitudinal temperature and equilibrium velocity) of the plasma stream varies over the cross-section of the stream which moves along an external magnetic field. Collisionless damping of surface waves in a semi-infinite isotropic plasma has been considered.

Surface Waves on a Plasma Half-Space

The effect of density gradients and a finite temperature on the dispersion relation for surface waves on a plasma half-space has been investigated analytically. The full set of Maxwell's equations is used to obtain the dispersion of surface waves on a warm homogeneous plasma, thus complementing earlier work on the electrostatic mode. The full surface-wave dispersion relation is then derived for a cold plasma with arbitrary but weak density profile in the WKB limit. Finally, the dispersion of electrostatic surface modes on a cold plasma with a linear density profile of arbitrary strength is obtained. It is shown that when the density variation over a wavelength is very large, a new type of damped surface wave with a frequency higher than the surface plasma frequency is possible.

Elastic Surface Waves in Crystals

Elastic surface waves in a general semi-infinite, anisotropic medium are discussed in terms of a six-dimensional vector formalism. The six-dimensional state vectors have the physical significance that their first three components constitute the displacement of and their last three components the force on the surface of the medium. For a semi-infinite medium with no sources of energy in its interior, a definite relation exists between force and particle velocity at the surface. This relation defines an impedance matrix for the semiinfinite medium which is a function of frequency, wave vector, and material parameters. The impedance matrix exhibits interesting symmetry properties and provides us with some generally valid relations for surface waves. In particular, formulas for energy and power relations attain attractive forms especially suitable for numerical computation. Finally, some characteristic properties of surface waves along free surfaces are discussed, including undamped and damped ("leaky") surface waves.

Waves and Instabilities in a Finite Plasma

A dispersion relation is derived for electrostatic waves in a plasma confined between planes which perfectly reflect the particles but have no effect on the fields. A uniform magnetic field perpendicular to the planes is assumed. Both classical and quantum-mechanical derivations are given. In the quantum-mechanical derivation some terms appear which do not appear in the classical derivation. These terms are due to finite de Broglie wavelength of the particles. The classical dispersion relation is applied to the investigation of volume and surface plasma oscillations and volume and surface ion sound waves in an unmagnetized plasma and to volume waves in magnetized plasmas. Volume waves are characterized by a discrete set of parallel wavenumbers. The damping or growth of volume waves is nearly the same as that of a corresponding infinite plasma wave. The damping of surface waves is quite different.

Damping of surface (sound) waves by the air

The letter relates to the substitution of e.m. circuit elements by transducers and, for example, sound-wave delay elements. Experimental and theoretical considerations suggest, however, that, with surface (sound)-wave elements, reradiation into the air can augment substantially the attenuation already existing owing to internal friction and scattering.

Surface-wave damping in closed basins

The damping of surface waves in closed basins appears to be due to ( a ) viscous dissipation at the boundary of the surrounding basin, ( b ) viscous dissipation at the surface in consequence of surface contamination, and ( c ) capillary hysteresis associated with the meniscus surrounding the free surface. Boundary layer approximations are invoked in the treatment of ( a ) and ( b ) to reproduce and extend results that have been obtained previously by more cumbersome procedures. The surface film is assumed to act as a linear, viscoelastic surface and may be either insoluble or soluble; however, the relaxation time for the equilibrium of soluble films is neglected relative to the period of the free-surface oscillations. Capillary hysteresis is analysed on the hypothesis that both the advance and recession of a meniscus are opposed by constant forces that depend only on the material properties of the three-phase interface. The theoretical results for the logarithmic decrements of gravity waves in circular and rectangular cylinders are compared with the decay rates observed by Case & Parkinson and by Keulegan, which typically exceeded the theoretical value based on wall damping alone by factors of between two and three. It is concluded that both surface films and capillary hysteresis can account for, and are likely to have contributed to, these observed discrepancies. The theoretical effect of a surface film on wind-generated gravity waves is examined briefly and is found to be consistent with the observation that the addition of detergent to water can increase the minimum wind speed (required to produce waves) by one order of magnitude.

Mie Theory and the Glory*

Results are presented of the predictions of Mie’s series solution to the scattering of an electromagnetic plane wave from a dielectric sphere of index 1.333. Cases of size parameters near 200 and 500 are examined in detail in an attempt to understand the mechanism responsible for the backscattering of light. These calculations demonstrate that the backscattering is due mainly to the last few significant terms in the Mie expansion, which can be associated with geometrical rays grazing the droplet surface, or “surface waves.” Sharp periodic spikes in the dependence of the backscattered intensity are shown to be associated with very slightly damped surface waves of both polarizations involving hundreds of circumvolutions. The geometrically computed axial contribution to the backscattered light is shown to be present in the Mie results.

Viscous damping of gravity waves over a permeable bed

The damping of small-amplitude surface waves on a viscous fluid over a permeable fixed bed is studied. Conservation arguments and consideration of the rate of doing work at the fluid-bed interface are applied in a careful analysis of the boundary conditions at the interface. It is shown that stresses are not continuous at the interface. A general dispersion relationship, which gives the damping characteristics for given wave parameters, is found together with the stream functions for the flow in the two regimes. The wave damping characteristics are different from those given in previous studies of waves over a permeable fixed bed and are a consequence of the new boundary conditions derived below. The damping effects due to percolation in the fixed bed are not always small in comparison with the viscous effects. Some numerical examples of typical situations are given.

Damping of surface waves in an incompressible liquid

The damping of surface waves of small amplitude in liquid contained in cylinders has been calculated. Viscous dissipation in an assumed laminar boundary layer was taken to be the primary cause of damping. Experimental results were obtained for the logarithmic decrement as a function of the ratio of liquid height to cylinder radius for several water-filled cylinders. Theory and experiment were found to be in good agreement.