Reflection analysis for nonlinear shoaling waves with an opposing current

The present study investigates the nonlinear interaction between shoaling regular surface gravity waves and opposing, collinear background currents over a mildly sloping bottom, up to conditions approaching wave blocking, defined as the regime in which the wave-energy flux ceases to propagate upstream against an opposing current. The paper proposes a reflection-analysis model for decomposing the measured wave field into incident and reflected components under spatially varying bathymetry and current conditions. The model combines a WKB-type propagation framework, current-modified dispersion relations, wave-action-based amplitude modulation, and a nonlinear harmonic decomposition aimed at distinguishing bound contributions from higher-order residual components compatible with free propagation. The method is restricted to regular or sufficiently narrow-banded wave fields and is not presented as a general decomposition method for broadband field conditions. A second objective is to examine how the blocking and near-blocking response varies among deliberately different imposed current-profile configurations and how nonlinear harmonic content contributes to the measured reflection response. Particular attention is devoted to differences among the flow-conditioner cases, bathymetric variation, the nonlinear harmonic composition of the wave field, and the identification of blocking regions for higher-order residual harmonics. The framework is tailored to waves propagating against opposing currents at river mouths and coastal inlets with mild bottom slopes, where substantial deviations from classical linear reflection theory are anticipated. The estimated reflection response varies with the strength of the opposing flow, the imposed flow-conditioner configuration, and the nonlinear wave–current interaction processes that develop near blocking. Because the dispersion model uses a depth-averaged current and does not resolve vertical shear, differences among flow-conditioner cases are interpreted as experimental associations rather than as a direct quantitative isolation of shear effects. The results indicate that current-driven shoaling and near-blocking conditions can locally modify reflected energy within estuarine transition regions and thereby contribute to hydrodynamic forcing during energetic and extreme events.