Estimation of Hydrodynamic Modulation Transfer Function for the Creamer and Choppy Wave Surface Models

Scattering simulations from time-varying ocean-like surfaces are sensitive to non-linear hydrodynamic effects in water wave propagation. Two approaches to introduce such nonlinearities – the Creamer transform and the Choppy wave model (CWM) – are commonly considered but lead to differing simulated Doppler spectra. A Modulation Transfer Function-based theory could explain the discrepancies if the two models yielded different hydrodynamic modulations of small scattering ripples by larger underlying waves. We perform 2D numerical experiments to measure the hydrodynamic modulation transfer function (HMTF) for either model. Two distinct techniques are employed – one limits the large-scale structure to a solitary sinusoidal wave, and another is designed to work with full-spectrum ocean-like surfaces. Both techniques reveal that Choppy-wave HMTF values are significantly lower than their Creamer counterparts, which apparently contributes to the Doppler centroid differences observed in scattering simulations. The CWM HMTF is also lower than available analytical results, while the Creamer transform-induced hydrodynamic modulation is close to or exceeds those predictions. More work is required to determine a preference of one model over the other.