Energy flux for trains of inhomogeneous plane waves

1980 ◽  
Vol 370 (1742) ◽  
pp. 417-429 ◽  
Keyword(s):  
Energy Flux ◽  
Energy Equation ◽  
Plane Waves ◽  
Frequency Dispersion ◽  
Conservation Of Energy ◽  
Inhomogeneous Plane ◽  
Wave Trains ◽  
The Mean ◽  
Point Form ◽  
Inhomogeneous Plane Waves

The propagation of inhomogeneous plane waves in linear conservative systems is considered. It is assumed that the secular equation governing the propagation of a plane wave of slowness S has the form Q ( S ) = 0 where Q is independent of frequency. Dispersion enters via the boundary condi­tions. By using the point form of the conservation of energy equation results are obtained which relate the mean energy flux vector R ˜ with the mean energy density Ẽ for any number of wave trains. In particular for a single train of inhomogeneous plane waves it is shown that R ˜ . S + = Ẽ . The results are relevant in electromagnetism, elasticity and fluid dynamics.

scholarly journals Energy flux for plane waves in linear conservative systems

1977 ◽  
Vol 20 (1) ◽  
pp. 106-113 ◽  
Author(s):  
M. Hayes
Keyword(s):  
Energy Flux ◽  
Energy Equation ◽  
Plane Waves ◽  
Direct Proof ◽  
Flux Vector ◽  
Conservation Of Energy ◽  
Conservative Systems ◽  
The Mean ◽  
Point Form ◽  
Energy Flux Vector

AbstractThe point form of the conservation of energy equation is used to give simple and direct proof of results concerning the mean energy flux vector for systems of sinusoidal small amplitude waves in linear conservative systems. No constitutive equation is used explicitly.

scholarly journals Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190478
Author(s):  
N. H. Scott
Keyword(s):  
Energy Density ◽  
Energy Flux ◽  
Plane Waves ◽  
Time Averaging ◽  
Complex Frequency ◽  
Hereditary Viscoelasticity ◽  
Inhomogeneous Plane ◽  
Dissipative Material ◽  
Comparable Magnitude ◽  
Inhomogeneous Plane Waves

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency ω , and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency 2 ω . The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency ω . A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2 ω . It is shown that the complex group velocity is related to the amplitudes of the terms with frequency 2 ω rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.

scholarly journals New capabilities of Chetaev´s model

2016 ◽  
Vol 2 (2) ◽  
pp. 104-114
Author(s):  
Михаил Савин ◽  
Mihail Savin ◽  
Юрий Израильский ◽  
Yuriy Izrailsky
Keyword(s):  
Experimental Data ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Geomagnetic Pulsations ◽  
Energy Fluxes ◽  
Field Recordings ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Wave ◽  
S Model ◽  
Inhomogeneous Plane Waves

This paper considers anomalies in the magnetotelluric field in the Pc3 range of geomagnetic pulsations. We report experimental data on Pc3 field recordings which show negative (from Earth’s surface to air) energy fluxes Sz<0 and reflection coefficients |Q|>1. Using the model of inhomogeneous plane wave (Chetaev’s model), we try to analytically interpret anomalies of energy fluxes. We present two three-layer models with both electric and magnetic modes satisfying the condition |Qh|>1. Here we discuss a possibility of explaining observable effects by the resonance interaction between inhomogeneous plane waves and layered media.

Transient representation of the Sommerfeld‐Weyl integral with application to the point source response from a planar acoustic interface

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1495-1505 ◽  
Author(s):  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Point Source ◽  
Plane Waves ◽  
Transient Waves ◽  
Layer Boundary ◽  
Spherical Source ◽  
Time Harmonic ◽  
Starting Point ◽  
Inhomogeneous Plane ◽  
Acoustic Interface ◽  
Inhomogeneous Plane Waves

Point source responses from a planar acoustic and/or elastic layer boundary (as well as from a stack of planar parallel layers) are generally obtained by using as a starting point the Sommerfeld‐Weyl integral, which can be viewed as decomposing a time‐harmonic spherical source into time‐harmonic homogeneous and inhomogeneous plane waves. This paper gives a powerful extension of this integral by providing a direct decomposition of an arbitrary transient spherical source into homogeneous and inhomogeneous transient plane waves. To demonstrate with an example the usefulness of this new point source integral representation, a transient solution is formulated for the reflected/transmitted response from a planar acoustic reflector. The result is obtained in the form of a relatively simple integral and essentially corresponds to the solution obtained by Bortfeld (1962). It, however, is arrived at in a physically more transparent way by strictly superimposing the reflected/transmitted transient waves leaving the interface in response to the incident transient homogeneous and inhomogeneous plane waves coming from the center of the point source.

Inhomogeneous plane waves in layered materials including fluid, solid and porous layers

Wave Motion ◽  
1991 ◽  
Vol 13 (4) ◽  
pp. 329-336 ◽  
Author(s):  
Walter Lauriks ◽  
Jean F. Allard ◽  
Claude Depollier ◽  
André Cops
Keyword(s):  
Plane Waves ◽  
Layered Materials ◽  
Porous Layers ◽  
Inhomogeneous Plane ◽  
Inhomogeneous Plane Waves
Sign in / Sign up

Export Citation Format

Share Document