y-direction momentum
∂ 2v ∂ 2v ∂ 2v
∂v
∂v
∂v
∂v
1 ∂p
+u +v +w = -
+ v 2 + 2 + 2
ρ ∂y
∂t
∂x
∂y
∂z
∂x
∂y
∂z
acceleration terms
pressure term
viscous shear terms
(3)
( ) () ( )
∂
∂
∂
u ' v' +
v '2 +
-
v 'w'
∂x
∂y
∂z
turbulence terms
z-direction momentum
∂2w ∂2w ∂2w
∂w
∂w
∂w
∂w
1 ∂p
+u
+v
+w
=-
(- g + v ∂x2 + ∂y 2 + ∂z 2
ρ ∂z gravity
∂t
∂x
∂y
∂z
acceleration terms
pressure term
viscous shear terms
(4)
) () ()
∂
∂
∂
u ' w' +
w '2
-
v 'w' +
∂x
∂y
∂z
turbulence terms
where
t = time
z = vertical coordinate
u, v = nonturbulent horizontal components of velocity in the x and y
directions, respectively
u′, v′ = turbulent fluctuating components of velocity in the x and y directions,
respectively
w = nonturbulent vertical component of velocity in the z direction
w′ = turbulent fluctuating component of velocity in the z direction
p = fluid pressure
ρ = fluid density
ν = fluid kinematic viscosity
Appropriate scaling criteria are derived from the equations of motion by
expressing the equations in nondimensional form using the following definitions
and substituting for the independent and dependent variables:
26
Chapter 4 Turbulence Scale Effect in Distorted Models
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