Reynolds Equation and Mixing Length Model

Phenomenological Theories of Turbulence

Logarithmic Velocity Near a Wall

Near a wall, there is a region (inertial sublayer) where turbulence is characterized by a single length scale (distance from the wall ) and a single velocity scale

(shear velocity = ).

In this region,

,  = von Karman constant,

(22)

and the shear stress is about . Equation (19), then implies

,

(23)

or

.

(23)

Integrating Equation (24), it follows that

,

(25)

or

, , ,

(26)

where .