Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Energy Partition in the Reflection and Refraction of Plane Waves

J. Bazer and R. Burridge
SIAM Journal on Applied Mathematics
Vol. 34, No. 1 (Jan., 1978), pp. 78-92
Stable URL: http://www.jstor.org/stable/2100859
Page Count: 15
  • Subscribe ($19.50)
  • Cite this Item
Energy Partition in the Reflection and Refraction of Plane Waves
Preview not available

Abstract

We consider plane monochromatic wave motions governed by linear, first order, homogeneous, symmetric hyperbolic systems with constant coefficients in media separated by a plane interface. A homogeneous plane wave incident on such an interface produces, in general, both homogeneous and inhomogeneous reflected and refracted (derived) waves. At each point of the interface, we show that the normal component of the energy flux (e.g., Poynting's vector in electromagnetic theory) directed away from the interface is the sum of the corresponding components the energy fluxes associated with the separate homogeneous derived waves. In spite of the quadratic nature of the energy flux no cross terms arise and no energy is carried normal to the interface by the inhomogeneous plane waves. For "nondissipative" interface conditions the sum of the separate normal energy fluxes directed away from the interface is equal to the flux in the incident wave directed normally toward the interface, thereby validating the well known energy balance law for a large class of physical systems and interface conditions. Several illustrations are given from electromagnetic theory and continuum mechanics. Our results hold also for the leading term in the geometrical optics approximation when the interface is curved and the governing equations have variable coefficients. Inhomogeneous equations, with lower order terms of a certain kind, and other dispersive systems may also be treated by considering each frequency separately.

Page Thumbnails

  • Thumbnail: Page 
78
    78
  • Thumbnail: Page 
79
    79
  • Thumbnail: Page 
80
    80
  • Thumbnail: Page 
81
    81
  • Thumbnail: Page 
82
    82
  • Thumbnail: Page 
83
    83
  • Thumbnail: Page 
84
    84
  • Thumbnail: Page 
85
    85
  • Thumbnail: Page 
86
    86
  • Thumbnail: Page 
87
    87
  • Thumbnail: Page 
88
    88
  • Thumbnail: Page 
89
    89
  • Thumbnail: Page 
90
    90
  • Thumbnail: Page 
91
    91
  • Thumbnail: Page 
92
    92