PARAMETERIZING OVERWATER FRICTION VELOCITY AND SEA-SURFACE DRIFT CURRENT USING WAVE STEEPNESS

Abstract

Overwater friction velocity $\left(U_0\right)$ is a vital parameter in air-sea interaction, particularly for the momentum transfer across the air-sea interface including the generation of waves and drift currents ( $U_{\text {sea }}$ ). From operational viewpoints of geophysical fluid mechanics and dynamics such as the analysis and prediction of oil spill trajectory, $U_{\text {sea }}$ is an important parameter. In order to understand the characteristics of $U_*$ and $U_{\text {sea }}$, both wind speed ( $U_{10}$ at height of 10 meters) and wave parameters including the dimensionless wave steepness ( $H_s / L_p$, here $H_s$ is the significant wave height, $L_p\left(=1.56 T_p^2\right)$ is the dominant wave length and $T_p$ is the dominant wave period) must be taken into account. However, only few direct simultaneous measurements of all 4 parameters, $U_{10}, U_s, H_s$ and $T_p$ are available in the literature, particularly during tropical cyclones (TCs). In this paper, based on wave data for $H_s / L_p$ and indirect estimation of normalized friction velocity $U_* / U_{10}$, during Hurricanes Katrina, Ivan, and other TCs, it is found that $U_* / U_{10}=1.1 H_s / L_p$ +0.013 and $U_{\text {sea }} j U_{10}=0.53\left(1.1 H_s / L_p+0.013\right)$. The proposed explicit relation between the normalized friction velocity and the wave steepness is verified by both the direct measurements during the Southern Ocean Waves Experiment and the independent wind gust or turbulence intensity method during 6 hurricanes. The explicit relation between the normalized surface current and the wave steepness is validated by the direct measurements during Hurricane Ivan.

Received: September 24, 2025
Accepted: October 29, 2025