  Modeling ocean surface waves under complex ocean current conditions is of
crucial importance to many naval applications. For example, traveling ships and
underwater vehicles generate spatially heterogeneous currents behind them
through their drag and propeller motions. The strong currents can influence the
surface wave pattern in the ship wake. In this study, the nonlinear
interactions between waves and complex wake currents are investigated using
numerical simulations. An in-house code is developed for high-fidelity
simulations of a nonlinear phase-resolved ocean wavefield interacting with
subsurface currents. Several typical wake patterns are simulated using the
present numerical method, and the influence of complex currents on the waves is
analyzed quantitatively using theoretical solutions of wave-current
interactions. We also present a method for solving the inverse problem of
deducing the current field based on surface-wave data using machine-learning
techniques. A deep neural network is designed for processing spatial-temporal
surface wave data. Detailed analyses on the distributions of regression errors
and the training dataset-dependency show that the proposed neural network can
effectively deduce the current field.
