Ekman friction

The theoretically predicted dual cascade with two power-law regimes in the kinetic energy spectrum (Fig. 1.4) has been reproduced in numerical simulations and confirmed by laboratory experiments. In some of the experiments spectra steeper than k 3 was observed in the enstrophy cascade range. This deviation can be related to the presence of additional damping at large scales, the so-called Ekman friction. Since the theoretical description of this regime is very similar to the problem of chemical decay in smooth flows we will return to this later in Chapter 6. 

Figure 6.9 Comparison of power spectra of decaying scalar (x) and vorticity (+) from numerical simulation of a two-dimensional turbulent flow with Ekman friction. Inset shows the ratio Z(k)/Eg(k), which is roughly constant for large k. (From Boffetta et al. (2002))...

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

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. 

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