Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 276

( ) ( )

Uyzt (,,) = Uyz (,) + uyzt ,, = U + ky kz uyzt + + ,,

0 y z

( )

[5.1]

Vyzt ,, ) =

=

vyzt (,,)

Wyzt ( , ,) wyzt ( , ,)

Figure 5.1. Structural elements associated with quasi-streamwise
vortices in the inner sublayer

We can see that the components of the l o cal mean
vorticity in directions z and y are constant with and

Ω= k

y z

in this particular flow. The independence of the
velocity field in direction x decouples u and (, )

Ω=− k

z y

vw because

⎛ ⎞ ⎛ ⎛

2 2

⎞

∂ u ∂ u ∂ u ⎞ ∂ u ∂ u

+ + kv + + kw = ν +

⎜ ⎟ ⎜ ⎜ ⎟

⎟

y z

∂ t ∂ y ∂ z ∂ y

2

∂ z

2

⎝ ⎠

⎝ ⎠ ⎝ ⎠

2 2

∂∂ ∂ v v v 1 ∂ p ⎛ ∂ ∂ v v ⎞

[5.2]

+ v + w = − + ν +

⎜ ⎟ 2 2

∂∂ ∂ t y z ρ∂ y ∂ ∂ y z

⎝ ⎠

⎛

2 2

⎞

∂∂ ∂ w w w 1 ∂ p ∂ ∂ w w

+ v + w = − + ν +

⎜ ⎟

∂∂ ∂ t y z ρ∂ z ∂ ∂ y

2

z

2

⎝ ⎠