Phase velocity of gravity waves over prescribed shear counter-currents

The present study examines the evolution of the phase velocity of surface gravity waves propagating against an opposing current in the vicinity of wave-blocking conditions, defined as flow regimes in which the wave-energy flux can no longer propagate upstream relative to an adverse background current. We adopted a novel experimental technique by deploying passive devices (‘flow conditioners’), which offer robust and repeatable control over the current profile to represent several shear structures. The classical evaluation of phase velocity through cross-correlation of wave-gauge signals is used as a reference for testing a novel experimental method based on high-resolution velocity fields obtained by particle image velocimetry. The two experimental estimates show generally good agreement. The experimental data are compared with theoretical predictions obtained from eigenvalue-based approximation schemes for the governing problem and with the full numerical solution of the classical Rayleigh eigenvalue problem. Second-order approximation models give the best theoretical estimates, while results from the full numerical solution are slightly more dispersed. The hypothesis of a uniform current largely underestimates the experimental values and breaks down systematically. Our results indicate that bulk current strength alone is insufficient to characterise the wave kinematics and that the vertical distribution of the adverse current within the wave-active layer exerts a significant additional influence. This helps explain why shear-weighted dispersion approximations perform well, contrary to the uniform-current assumption. This work is particularly relevant for the full-scale characterisation and prediction of compound flooding events arising from the combination of river flood discharges with intense marine storm conditions, offering quantitative considerations on the best predictive models that can be used in practical situations.