Turbulent diffusion coefficients in GLS scheme

I use GLS closure turbulent scheme.
I found that in most cases turbulent diffusion coefficients (AVT and AVM) are 0 at lower model levels.
As far as I understand,in GLS scheme if stratification is stable AVT and AVM should be small values but not 0.
Am I rigth?

Which is why there is a background diffusion/viscosity…