Getting to know turbulence - Turbulence in the Atmosphere - page 47

c final c initial

Figure 2.5 Diffusion of dye in a tank of turbulent fluid. The initial state is the
motionless one in Figure 2.4 . The top panel is an artist's sketch (motivated by Van
Dyke's (1982) photographs) of an instantaneous cross section shortly after the onset
of turbulence. The bottompanel shows the time evolution of the ensemble-averaged
dye concentration profile.

experiment - evolves qualitatively like the concentration in the molecular diffu-
sion problem. But it does so much more rapidly, so we'll use a much larger eddy
diffusivity K in the diffusion equation (2.75) ,

K ∂ 2 C

∂C
∂t =

∂z 2 .

(2.76)

The time τ t required for turbulent mixing is then τ t ∼ d 2 /K .