Ekman spiral

FIGURE 21.7 Variation of wind direction with altitude (a) balance of forces among pressure gradient, Coriolis force, and friction (b) the Ekman spiral. 

I Horizontal and Vertical Flows The relationship between horizontal and vertical velocities is embodied in the mass continuity equation 

Atmospheric flows are such that the horizontal mass flux divergence, the second and third terms on the LHS of (21.10) are essentially balanced by the fourth term, the vertical mass flux divergence. Thus 

When flow converges at lower levels, it flows vertically upward in such a way so as to satisfy (21.11), If we consider a column of air and integrate the last term on the LHS of (21.11) from the bottom (b) of the column to its top (/), we get 

Atmospheric measurements in a variety of circumstances show that the RHS of (21.13) generally has a magnitude of order 10 cm s 1 in the midtroposphere. (Updraft rates in cumulonimbus clouds can, however, reach values of 5ms. ) 

---

The upper ocean wind-driven current was described realistically for the first time by Walfried Ekman s landmark theory of 1905. The velocity distribution in the near surface layer of the ocean cannot be determined without additional information about the variation of the Reynolds stress vector with depth. Ekman (1905) assumed the Reynolds stress vector to be equal to the vertical shear of the mean current vector times a constant vertical eddy viscosity. The resulting current profile below the sea surface is the well known Ekman spiral with current speed decreasing exponentially with depth and current direction turning clockwise linear with depth from 45° right-handed to the wind stress vector at the sea surface. 

Many attempts have been made to verify Ekman s theory with observations. Clockwise turning mean current spirals that decay smoothly with depth have been observed by numerous investigators (Davis et al., 1981 Weller, 1981 Price et al., 1986, 1987 Weller et al., 1991 Rudnick and Weller, 1993 Wijffels et al., 1994 Chereskin, 1995 Lee and Eriksen, 1996 Weller and Plueddemann, 1996). Several ofthem observe a spiral thatis much flatter than an Ekman spiral in that the observed current rotates less with depth than predicted by Ekman s theory. 

As a result of these frictional effects, the wind direction commonly turns with height, as shown in Figure 21.7. The variation of wind direction with altitude is known as the Ekman spiral. Derivation of the expression for the Ekman spiral is the subject of Problem 21.2. 

C The Ekman spiral describes the variation of wind direction with altitude in the planetary boundary layer. The analytical form of the Ekman spiral can be derived by considering a two-dimensional wind field (no vertical component), the two components of which satisfy... 

---