Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 86

and

⎧ ⎫

2 2 2 2

⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠ ⎛ ⎝ ⎞ ⎠

⎪ ⎪

∂ u 1 ∂ u 1 ∂ u 2

∂

∂ u 2 *

[2.46]

ε Kax 2 = ν ⎨ − + 2 + 2 + 8 ⎬

⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟

∂ x 1 ∂ x 2 x 1 ∂ x 2

⎪ ⎪

⎩ ⎭

*

ε *

*

ε * Figure 2.10. Distribution of a) ε Kax 2 (equation [2.46]),b) ε Kax 1

ε * according to [ANT 91].
For the key, see Figure 2.9

*

(equation [2.45]) and c) ε K iso

The expression [2.46] is a good approximation of
dissipation for y + >

20 , as shown in Figure 2.10. This relation

overestimates

ε * near to the wall, but the error caused is

*

less than 0 . Both

relations [2.45] and [2.46] represent good approximations at
y + ≥

, which tends toward zero as y

ε

→

Kax 1

40 . Axisymmetry is no longer valid in and below the
buffer sublayer. The approximation

2

⎛ ⎞

5
4 ν

∂ u

*

ε ≈

⎜ ⎟

Kw

∂ y

⎝ ⎠

[2.47]

works relatively well in the viscous sublayer but not in the
buffer sublayer.