A non-dimensional wall distance for a wall-bounded flow can be defined in the following way:
Where
- u_* is the friction velocity at the nearest wall,
- y is the distance to the nearest wall and
- \nu is the local kinematic viscosity of the fluid.
y+ is often referred to simply as y plus and is commonly used in boundary layer theory and in defining the law of the wall.
y+ is a non-dimensional number similar to local Reynolds number, determining whether the influences in the wall-adjacent cells are laminar or turbulent, hence indicating the part of the turbulent boundary layer that they resolve.
The physical meaning is that if u have a turbulent flow, for a y+<5, which is very close from the wall, there is a region called viscous sublayer where the flow is laminar. This region only knows viscous stresses. u+=y+
when 5<y+<30: buffer layer , intermediate region
30<y+<500 (the upper limit can vary from a flow to another): log-region: turbulent stresses became dominant. u+=2.44 ln y+ + 5.5
The velocity profile here is not as much universal as in the viscous sublayer. It does not hold for cases with adverse pressure gradients....If the wall is not smooth, u must change the constants....
(the width of the log-layer is about 1/3 from the boundary layer: the rest is called defect region, and there exists correlations for veloity profile there for equilibrium boundary layers)
In CFD simulations, you can resolve the whole bounday layer and in such case, it need a very fine mesh near the walls (gradients are very important there). This approach is expensive. (u must have y+=1 on the first near wall cell)
You can instead use the wall law: choose the first cell to be in the log-law layer, and you dont need to resolve the whole boundary layer. This approach is more economical. However, it can lead to better results than the first one sometimes (if u are modeling the boundary layer with a non-suitable equation by exemple: case very frequent when u use the k-epsilon model)
