The propagation paths of oceanic internal tides are partly determined by their interaction with balanced flows, which are ubiquitous in the ocean. We make two efforts to better quantify and understand this interaction. In the first we examine the scattering effect that an isolated (cyclo)geostrophic vortex has on a rotating shallow-water plane wave. We run a suite of simulations in which we vary the non-dimensional vorticity of the vortex, Ro, the relative scale of the vortex size to the Rossby radius of deformation, Bu, and the size of the vortex compared to the internal tide wavelength, K, to observe how much energy is scattered by the vortex. Three-dimensional fits show that the percentage of scattered energy is proportional to Ro^{1.5} Bu^{-1.5/2} K^2. The second effort uses a deep learning algorithm (Pix2Pix) to disentangle waves and balanced flows from snapshots of Boussinesq simulations. We find good performance for mesoscale flows (Ro<<0.1), the algorithm will generate a wavefield which has up to a 0.97 correlation compared to the true wave field. This method is expected to be useful for satellite altimeters which only take snapshots of the sea surface height and require this disentanglement to infer ocean currents.