DNS and Analytical Modeling of Wave Evolution under Opposing Currents

Strong opposing currents create significant hazards to ship traffic by generating short and steep waves. This phenomenon, driven by the Doppler-shift effect, leads to critical wave-current interactions in ocean and coastal environments. Existing theoretical models for predicting wave characteristics under opposing currents show clear deviations from experimental observations. To address this gap, we perform direct numerical simulations (DNS) that fully resolve the Navier-Stokes equations, capturing the evolution of waves under adverse current conditions. These simulations are validated against recent experimental data from Zhou et al. (2023), showing acceptable agreement and highlighting the significant deviations from existing theories. Through a higher-order analytical analysis and a parametric DNS study, an improved theoretical model is derived, utilizing empirical curve fitting of the DNS data to describe wave modulation under opposing currents. The resulting model aims to reduce the observed deviations between existing theories and experiments. This work advances the fundamental understanding of wave transformation and breaking in strong current conditions, offering crucial implications for ocean engineering design and environmental modeling.