Revisiting the Definition of the Drag Coefficient in the Marine Atmospheric Boundary Layer

Abstract

A new functional form of the neutral drag coefficient for moderate to high wind speeds in the marine atmospheric boundary layer for a range of field measurements as reported in the literature is proposed. This new form is found to describe a wide variety of measurements recorded in the open ocean, coast, fetch-limited seas, and lakes, with almost one and the same set of parameters. This is the result of a reanalysis of the definition of the drag coefficient in the marine boundary layer, which finds that a constant is missing from the traditional definition of the drag coefficient. The constant arises because the neutral friction velocity over water surfaces is not directly proportional to the 10-m wind speed, a consequence of the transition to rough flow at low wind speeds. Within the rough flow regime, the neutral friction velocity is linearly dependent on the 10-m wind speed; consequently, within this rough regime, the new definition of the drag coefficient is not a function of the wind speed. The magnitude of the new definition of the neutral drag coefficient represents an upper limit to the magnitude of the traditional definition.

On the parameterization of the drag coefficient in mixed seas

“…It can be seen in Figure 6 that the observed friction velocity shows a linear dependence on wind speed for values greater than 7 m s -1 , which coincides with Therefore, the IntOA data seems to support the hypothesis of Foreman and Emeis (2010). However, in terms of C D the parameterization of Foreman and Emeis (2010) with C m =0.051, U 0 =8 m s -1 and u *0 =0.27 m s -1 (see Table 1) underestimates the observed C D by more than 20% (Fig. 5b) and the correlation coefficient is reduced as compared with that obtained from a linear dependence of C D on wind speed (Table 2).…”

“…From their analysis, Foreman and Emeis (2010) found u *0 =0.27 m s -1 and U 0 =8 m s -1 . It can be seen in Figure 6 that the observed friction velocity shows a linear dependence on wind speed for values greater than 7 m s -1 , which coincides with Therefore, the IntOA data seems to support the hypothesis of Foreman and Emeis (2010).…”

“…From their analysis, Foreman and Emeis (2010) found u *0 =0.27 m s -1 and U 0 =8 m s -1 . It can be seen in Figure 6 that the observed friction velocity shows a linear dependence on wind speed for values greater than 7 m s -1 , which coincides with Therefore, the IntOA data seems to support the hypothesis of Foreman and Emeis (2010). However, in terms of C D the parameterization of Foreman and Emeis (2010) with C m =0.051, U 0 =8 m s -1 and u *0 =0.27 m s -1 (see Table 1) underestimates the observed C D by more than 20% (Fig.…”

“…The observed C D during the IntOA experiment can be well described by a constant a=0.023 (García-Nava et al 2009), as if it were from mature seas (Hara and Belcher 2004), although in high winds wind waves are underdeveloped and the wave age decreases as the wind speed increases. Recently, Foreman and Emeis (2010) suggested that the wind speed dependence of C D is due to the neglect of a constant in the expected linear relation between u * and U 10 rather than to an increase in z 0 with the wind speed. They proposed a new definition of friction velocity as…”

“…Taylor and Yelland 2001). Recently, Foreman and Emeis (2010) proposed a new functional form to represent the drag coefficient for moderate to strong winds where no wind speed dependence was determined. While their results approximate rather well with data sets reported in the literature, the swell influence was not explicitly included in the analysis and the sea state conditions considered were wind sea-dominated.…”