Experimental determination of radiated internal wave power without pressure field data

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.