4.6: Wind Stress

The wind, by itself, is usually not very interesting. Often we are much more interested in the force of the wind, or the work done by the wind. The horizontal force of the wind on the sea surface is called the wind stress. Put another way, it is the vertical transfer of horizontal momentum. Thus momentum is transferred from the atmosphere to the ocean by wind stress.

Wind stress $T$ is calculated from: $$T = \rho_{a} C_{D} U_{10}^{2} \nonumber$$

where $\rho_{a} = 1.3 \ \text{kg/m}^{3}$ is the density of air, $U_{10}$ is wind speed at 10 meters, and $C_{D}$ is the drag coefficient. $C_{D}$ is measured using the techniques described in Section 5.6. Fast response instruments measure wind fluctuations within 10–20 m of the sea surface, from which $T$ is directly calculated. The correlation of $T$ with $U_{10}^{2}$ gives $C_{D}$ (figure $\PageIndex{1}$).

Figure $\PageIndex{1}$: The drag coefficient as a function of wind speed $U_{10}$ ten meters above the sea. Circles: Measured values from Smith (1980). Triangles: Measured values from Powell, Vickery, and Reinhold (2003). The solid line is from eq $(\PageIndex{1})$ proposed by Yelland and Taylor (1996). The dashed line is from Jarosz (2007).

Various measurements of $C_{D}$ have been published based on careful measurements of turbulence in the marine boundary layer. Trenberth et al. (1989) and Harrison (1989) discuss the accuracy of an effective drag coefficient relating wind stress to wind velocity on a global scale. Perhaps the best of the recently published values are those of Yelland and Taylor (1996) and Yelland et al. (1998) who give:

$$\begin{align} & 1000 C_{D} = 0.29 + \frac{3.1}{U_{10}} + \frac{7.7}{U_{10}^{2}} \quad\quad \left(3 \leq U_{10} \leq 6 \ \text{m/s}\right) \\ & 1000 C_{D} = 0.60 + 0.071 U_{10} \quad\quad \left(6 \leq U_{10} \leq 26 \ \text{m/s}\right) \end{align} \nonumber$$

for neutrally stable boundary layer. Other values are listed in their table 1 and in figure $\PageIndex{1}$.