center

Assumption

The turbulence near the a wall/solid boundary is only affected by the flow conditions at the wall and is independent of the flow conditions far away.

In the Outer Layer, the Turbulence is not affected by the the turbulence in the inner layer due to the huge difference in the Length scales ()

Wall Units / Plus Values

Using the above assumption, a few flow variables are identified.

  • distance from the wall .
  • Mean velocity (or velocity profile) .
  • Shear stress at the wall .
  • Fluid Density .
  • Fluid kinematic viscosity . After performing dimensional analysis we derive two new dimensionless quantities

Dimensionless Distance

Easier to remember

Dimensionless Velocity

Where,

  • Distance from the wall
  • Friction Velocity
  • Length Scale in the Inner layer

Note: In theory, the is only a function of , i.e, the assumption.


References

  1. http://brennen.caltech.edu/fluidbook/basicfluiddynamics/turbulence/lawofthewall.pdf