Visualization of a surface wave in an elastic medium via the complex Poynting vector

The complex Poynting vector can be used to visualize not only the flow of energy in an elastodynamic solid, but also the wave itself passing through the elastic medium. Usually the time average of the Poynting vector over one cycle is obtained, but this only gives the time average of the energy flux through the medium. However the instantaneous elastodynamic Poynting vector can be used instead of the more usual time-averaged Poynting vector in order to follow the energy flow as a function of time. The instantaneous Poynting vector gives the instantaneous energy flux through the elastic medium. The imaginary part of the complex Poynting vector gives the difference in the peak rates at which energy is stored in the medium at that point. This has already been shown for the simpler case of the instantaneous Poynting vector in an acoustic medium [J. A. Mann III et al., J. Acoust. Soc. Am. 82, 17–30 (1987)]. Computer animations of the instantaneous Poynting vector for a Rayleigh surface wave in a variety of materials, as well as the real and imaginary parts of the complex time averaged vector field, will be shown.