Meteorology: Turbulence/Dimensionless Analysis

[AppeltjeBosheuvel]

Good afternoon,

I find it hard to understand friction velocity, shear stress, momentum and temperature scale. For a class, we are using MOST dimensionless analysis to find values of intensity for the turbulence. However, I'm struggling with the terms.

What exactly is friction velocity u*? My book only states it is a velocity scale.
I read online it is the same as shear velocity, when shear stress is rewritten in units of velocity (I assume so it is easier to make a dimensionless analysis later). But what exactly is shear stress though? Is is the stress of the resistance between a fast and slow moving air layer when it comes to turbulence? I find it hard to understand.

Functions given are u* = squareroot(surface shear stress)/density = squareroot(-u'w')
Where does the square root come from?

What exactly is T* temperature scale and q* moisture scale of water vapor?

I'm super confused. Thanks already!

 

[boneh3ad]

Welcome to the wonderful world of turbulence. Friction velocity (and similar scaling factors) don't always have meaningful physical interpretations. In this case, it's a velocity scale that is based on the wall shear stress. As far as I know, it has no other easily-parsed explanations.

 

[AppeltjeBosheuvel]

Thank you :)

 

[Chestermiller]

Good afternoon,

I find it hard to understand friction velocity, shear stress, momentum and temperature scale. For a class, we are using MOST dimensionless analysis to find values of intensity for the turbulence. However, I'm struggling with the terms.

What exactly is friction velocity u*? My book only states it is a velocity scale.
I read online it is the same as shear velocity, when shear stress is rewritten in units of velocity (I assume so it is easier to make a dimensionless analysis later). But what exactly is shear stress though? Is is the stress of the resistance between a fast and slow moving air layer when it comes to turbulence? I find it hard to understand.

Functions given are u* = squareroot(surface shear stress)/density = squareroot(-u'w')
Where does the square root come from?

What exactly is T* temperature scale and q* moisture scale of water vapor?

I'm super confused. Thanks already!

The surface shear stress is not equal to $\rho {u'w'}$.

 

[AppeltjeBosheuvel]

The surface shear stress is not equal to $\rho {u'w'}$.

So what does that meam?

 

[Chestermiller]

So what does that meam?

It means that, because of the no-slip boundary condition, the velocity fluctuations at the surface are zero. So only the viscous stress is present at the surface.

 

[AppeltjeBosheuvel]

Thank you