  Determination of energy transport is crucial for understanding the energy
budget and fluid circulation in density varying fluids such as the ocean and
the atmosphere. However, it is rarely possible to determine the energy flux
field $\mathbf{J} = p \mathbf{u}$, which requires simultaneous measurements of
the pressure and velocity perturbation fields, $p$ and $\mathbf{u}$. We present
a method for obtaining the instantaneous $\mathbf{J}(x,z,t)$ from density
perturbations alone: a Green's function-based calculation yields $p$, and
$\mathbf{u}$ is obtained by integrating the continuity equation and the
incompressibility condition. We validate our method with results from
Navier-Stokes simulations: the Green's function method is applied to the
density perturbation field from the simulations, and the result for
$\mathbf{J}$ is found to agree typically to within $1\%$ with $\mathbf{J}$
computed directly using $p$ and $ \mathbf{u}$ from the Navier-Stokes
simulation. We also apply the Green's function method to density perturbation
data from laboratory schlieren measurements of internal waves in a stratified
fluid, and the result for $\mathbf{J}$ agrees to within $6\%$ with results from
Navier-Stokes simulations. Our method for determining the instantaneous
velocity, pressure, and energy flux fields applies to any system described by a
linear approximation of the density perturbation field, e.g., to small
amplitude lee waves and propagating vertical modes. The method can be applied
using our Matlab graphical user interface EnergyFlux.
