The Dependence on Wave Age

Modification of the Charnock Wind Stress Formula to Include the Effects of Free Convection and Swell

“…Abdella and D'Alessio (2003) performed the numerical simulations including the convective velocity; they showed that their results of sea surface temperature and heat content are in good agreement with the observations. For young and developing waves, the wave-induced stress enhances the surface roughness; the surface roughness in the absence of swell derived in this paper is remarkably close, almost identical to the wind stress formula proposed by Volkov (2001). However, in this paper, the proposed formula for the aerodynamic roughness in the presence of heavy swell, deviated significantly from Volkov's formula, is for the first time theoretically derived and substantiated by experimental data; it shows that the surface roughness depends on the relative wave age.…”

“…(59) is remarkably close to the roughness formula (Eq. 60-1) proposed by Volkov (2001), considering the different approaches used to derive the surface roughness lengths; the two curves are almost identical to each other. However, under the conditions of strong swell, the two curves diverge significanly.…”

“…The data in Fig. 4 show that under the influence of swell, the surface roughness is much less than the value of 0.008 proposed by Volkov (2001). That is, under the influence of heavy swell, Eq.…”

“…(57-2) shows that the sea surface is very smooth, much smoother than suggested by Volkov (2001), i.e., there exits a "super" smooth sea surface. Equations (35), (38), (39), (46), (49), (54), (56), (57), and (59) are the main results of this paper.…”

“…The semi-empirical formulas of the surface roughness suggested by Volkov (2001) (59) and Eq. (60-1) with experimental data is given in Fig.…”