General Points - Transport and Coherent Structures in Wall Turbulence - page 16

in the Reynolds equation. As previously indicated, and a
fortiori in the above representation, it is clear that

− ρ uv

plays the physical role of a stress. The R ey nolds stress is
positive in a flow where the gradient ∂∂> Uy 0 , and it

increases the total stress.

Thus, the stress is added to the viscous stress to

− ρ uv

yield the total stress τ . One typical way to model is

− ρ uv

tot

to link it to the average gradient Uy , because, without

shear, no turbulence is produced. We then introduce a
fictitious viscosity,

∂∂

()

, called the eddy (or turbulent)
viscosity, and express the Reynolds stress as

ν

t y

∂ U

()

[1.23]

−= uv ν y

t

∂ y

()

is not strictly linked to vortices,
although coherent vortex structures, particularly near to the
wall, play an important part in generating turbulence. The
turbulent viscosity is not a physical property of the fluid -
far from it. It is not a constant, and varies spatially. There is
no universal model for

The eddy viscosity

ν

t y

()

, and it depends on the
phenomenology of the particular flow.

ν

t y

Thus, the total stress can be written as

∂ U

()

τ = ρνν ⎡ + y ⎤

⎣ ⎦

tot t

∂ y

Essentially, we can distinguish two zones in a wall layer,
depending on whether the eddy viscosity is greater or lesser
than the kinematic viscosity. The kinematic viscosity is
predominant in a confined sublayer near to the wall, where