Poynting vector of a scalar wave Consider a scalar wave (of sound for example) of the form $\psi(\vec{r},t)$. Which is its Poynting vector? I mean, the vector that takes account for the energy flux in the same sense as for the case of an electromagnetic wave.
 A: As a fast answer I would point out that the Poynting vector is just the spatio-temporal components of the electromagnetic stress-energy tensor. So for a scalar wave, or in general for a scalar field, $\phi$ , you would like to search there. For example, the energy-momentum tensor for the real Klein-Gordon field is:
\begin{equation}
\Theta_{\mu \nu} = \partial_\mu \phi \partial_\nu \phi - \frac{1}{2} \eta_{\mu \nu} \left( \partial^\sigma \phi \partial_\sigma \phi + m^2 \phi^2\right)
\end{equation}
where $\partial_\mu = \partial / \partial x^\mu$, $\eta_{\mu\nu}$, is the Minkowski metric and $m$ is the mass of the field. The spatio-temporal components of this tensor are just (the dot denoting temporal derivative, and latin subscripts spatial components):
\begin{equation}
\Theta_{0 i} = \partial_0 \phi \partial_i \phi = \dot{\phi}\partial_i\phi
\end{equation}
which is just the fields linear momentum density $\mathcal{P}_i = \Theta_{0i}$, as in the electromagnetic case:
\begin{equation}
\mathcal{P}_i^{EM} = \frac{S_i}{c^2} =-\frac{T_{0i}}{c}
\end{equation}
(maybe wihtout the minus sign), here $S_i$ is the Poynting vector and $T_{0i}$ the spatio-temporal components of the electromagnetic energy-momentum (or stress-energy) tensor.
Hope I clarified some ideas!
kl0z.
