  We present a method to determine, using only velocity field data, the
time-averaged energy flux $\left<\boldsymbol{J}\right>$ and total radiated
power $P$ for two-dimensional internal gravity waves. Both
$\left<\boldsymbol{J}\right>$ and $P$ are determined from expressions involving
only a scalar function, the stream function $\psi$. We test the method using
data from a direct numerical simulation for tidal flow of a stratified fluid
past a knife edge. The results for the radiated internal wave power given by
the stream function method agree to within 0.5% with results obtained using
pressure and velocity data from the numerical simulation. The results for the
radiated power computed from the stream function agree well with power computed
from the velocity and pressure if the starting point for the stream function
computation is on a solid boundary, but if a boundary point is not available,
care must be taken to choose an appropriate starting point. We also test the
stream function method by applying it to laboratory data for tidal flow past a
knife edge, and the results are found to agree with the direct numerical
simulation. Supplementary Material includes a Matlab code with a graphical user
interface (GUI) that can be used to compute the energy flux and power from any
two-dimensional velocity field data.
