Observations of the directional distribution of the wind energy input function over swell waves

Abstract

Field measurements of wind stress over shallow water swell traveling in different directions relative to the wind are presented. The directional distribution of the measured stresses is used to confirm the previously proposed but unverified directional distribution of the wind energy input function. The observed wind energy input function is found to follow a much narrower distribution ( β∝cos⁡3.6θ) than the Plant (1982) cosine distribution. The observation of negative stress angles at large wind‐wave angles, however, indicates that the onset of negative wind shearing occurs at about θ≈ 50°, and supports the use of the Snyder et al. (1981) directional distribution. Taking into account the reverse momentum transfer from swell to the wind, Snyder's proposed parameterization is found to perform exceptionally well in explaining the observed narrow directional distribution of the wind energy input function, and predicting the wind drag coefficients. The empirical coefficient (ε) in Snyder's parameterization is hypothesised to be a function of the wave shape parameter, with ε value increasing as the wave shape changes between sinusoidal, sawtooth, and sharp‐crested shoaling waves.

Deviation of Wind Stress From Wind Direction Under Low Wind Conditions

“…Based on the eddy covariance method, which has been widely utilized (Aubinet et al, ), the wind stress at a given height above the surface can be represented by the following: Here τ x is the longitudinal or downwind stress; τ y is the lateral or crosswind stress; 〈 〉 is a time or spatial averaging operator that represents the Reynolds average; and u ′ , v ′ , and w ′ are the longitudinal, lateral, and vertical velocity fluctuations, respectively (Grachev et al, ). Moreover, τ x and τ y can be represented by τ x = ρ a C Dx U 2 and τ y = ρ a C Dy U 2 , respectively, referring to the coordinate framework of Shabani et al (). Here ρ a is the air density, U is the wind speed, and C Dx and C Dy are the downwind and crosswind drag coefficient, respectively.…”

“…, v 0 , and w 0 are the longitudinal, lateral, and vertical velocity fluctuations, respectively (Grachev et al, 2003). Moreover, τ x and τ y can be represented by τ x = ρ a C Dx U 2 and τ y = ρ a C Dy U 2 , respectively, referring to the coordinate framework of Shabani et al (2016). Here ρ a is the air density, U is the wind speed, and C Dx and C Dy are the downwind and crosswind drag coefficient, respectively.…”

Increased Aerodynamic Roughness Owing to Surfzone Foam

“…Continuous measurements for four weeks in May-June 2016 were divided into 15-min blocks for analysis. The analysis for computing momentum fluxes and procedures for quality controlling the data is given in Aubinet et al (2012), which is similar to that described by Shabani et al (2014) and Ortiz-Suslow et al (2015).…”

“…Anctil and Donelan (1996) found increased C d values for waves shoaling from 12 m to breaking in 2-m water depth. Shabani et al (2014Shabani et al ( , 2016 found that measured C d for near-neutral, atmospheric stability over the shoaling region and surfzone were O(2) times larger than open-ocean estimates, which they ascribe to the wave celerity c and shape effects. Similar to Anctil and Donelan (1996), they suggested that as the wave shoals, wave speed slows relative to the wind speed U increasing C d .…”

Interaction and growth of low frequency and high frequency wind waves

“…These provided 3D turbulent velocity measurement, which digital signal was fed into the data logger and logged synchronously with other instruments. This was the same wind measurement and logging equipment as was used by Shabani et al (2014) and Shabani et al (2016), although deployed at a different location, using a different support structure and positioned at different elevations.…”