Growth of wind-driven waves under uniform currents

Abstract

This study experimentally investigated the growth of wind-driven waves under uniform currents. The wind-driven wave spatiotemporal evolution characteristics were collected along the fetch, and visual techniques were used to measure the phase velocity and flow field characteristics. Based on the experimental results, the variation patterns of dimensionless peak frequency and energy over time and space were analyzed, and their relationships with the dimensionless current velocity, fetch, and wave age were determined. The currents significantly influence the trend in dimensionless energy, with their effect on peak frequency and dimensionless energy primarily reflected in the exponential term. The exponent coefficient of peak frequency for the co-current is approximately $U_c/u^{\ast }$, while for the counter-current, it is $6{\chi }^{\ast -0.26}{U}_c/u^{\ast }$, where $U_c$ is the current velocity, $u^{\ast }$ is the wind friction velocity, and ${\chi }^{\ast }$ is the dimensionless fetch. Both co- and counter-currents increase the turbulent kinetic energy. The co-current minimally affects the velocity field distribution, with the Q4 quadrant dominating in the quadrant analysis. In contrast, the counter-current significantly alters the velocity field, shifting the Reynolds stress dominance from Q4 to Q2 and resulting in a more evenly distributed four-quadrant pattern, enhancing the upward momentum transfer. These changes in momentum transfer significantly affect the spatiotemporal evolution of wind-driven waves under uniform currents.