Hello,
What you plan to do is not very clear. A turbulence model gives the turbulent viscosity, so its own sensitivity to this viscosity is a weird concept... do you mean sensitivity to the molecular viscosity ?
Anyway if you look at subroutine smago.f you will see a hardcoded constant, and you can study the sensitivity to this constant.
An important thing to understand is that in 2D the diffusion coefficient should include also the dispersion due to the heterogeneity of velocities on the vertical. Only the Elder model adds this dispersion to the longitudinal viscosity. All other models neglect this aspect.
With best regards,
Jean-Michel Hervouet