On the wave age dependence of wind stress over pure wind seas

TLDR

The dataset spans a wide range of wave ages with significant variability in friction velocity and wave phase speed. The study investigates how wave age influences wind stress under Monin‑Obukhov similarity scaling. Data from five recent field campaigns covering pure wind sea, deep water, and fully rough flow conditions were used. The study finds that surface roughness scales as \(z_o/\sigma = 13.4 (u^*/c_p)^{3.4}\), showing a strong dependence on wave age that aligns with Charnock‑based formulations.

Abstract

Data from five recent field campaigns are selected for pure wind sea, deep water, and fully rough flow conditions. The combined data set includes a wide range of wave ages, with high variability in both friction velocity and wave phase speed. These data, which are expected to follow Monin‐Obukhov similarity scaling, are used to investigate the influence of wave age on wind stress. The relationship between the dimensionless roughness and inverse wave age is found to be z o /σ = 13.4 ( u * / c p ) 3.4 , where z o is the surface roughness length, σ is the standard deviation of the surface elevation, u * is the friction velocity, and c p is the wave phase speed at the peak of the spectrum. This relationship, which represents a significant dependence of roughness on wave age, was obtained using a procedure that minimizes the effects of spurious correlation in u * . It is also shown to be consistent with the wave age relationship derived using an alternate form of the dimensionless roughness, namely, the Charnock parameter z o g / u * 2 , where g is the gravitational constant.