Scale Separated Approaches to the Interaction of Oceanic Internal Waves, part II: A one-dimensional numerical model

We present an idealized representation of high frequency oceanic internal waves propagating in a background field of inertial waves. This report follows a companion paper in which we present derivations for transport equations using both wave turbulence theory and path integral techniques. These differ, with the path integral transport equation explicitly acknowledging a mean drift of wave packets to smaller scales. Neither prediction for the net downscale transport of energy compares well with observations. Here we compare ray tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and using path integral techniques. At small inertial wave amplitudes, all three provide consistent descriptions for the mean drift and dispersion about that mean drift. At oceanic amplitudes, however, the numerics support diminished transport and dispersion. This coincides with the mean drift time scale becoming similar to the correlation time scale, which we parse as the signature of a transition to a non-Markovian process. espite this decrease, estimates of downscale energy transfer are still significantly larger than expected from oceanic derived metrics. We offer the hypothesis that differences between the ray-path formulation and observations results from an unwarranted discard of Bragg scattering resonances that reduce the mean drift