Wave energy analysis
The transport of wave energy in the timeharmonic field can be visualized by the energy streamlines, which show the trajectories of timeaveraged energy fluxes. At every point energy streamlines are tangential to the power density vector introduced by Umov for elastodynamic fields in 19th century. Its components can be calculated via the displacement and stress representations. Analysis of energy distribution gives deep insight into physics, it is sufficient for investigation of resonance phenomena and localization, especially scattering on inhomogeneities.

A timeaveraged energy flux E across a surface S in the timeharmonic elastic wave field u(x) is introduced as an integral of the normal to S component of the averaged power density vector (UmovPoynting vector) e(x) over S:Averaged power density vector is calculated as scalar product of displacement and stress vectors:while n is the unit outward normal for S. Continuous vector field e(x) determines in the space x a set of noncrossing curves x(s) to which e(s) is tangential at any point.It has been known that there exist zones in the timeaveraged energy flows in which the streamlines are closed. Centers of these zones, named energy vortices, are points of wavefront dislocations at which e=0. 