Dear Andrei,

the friction velocity is fixed by the pressure gradient dp/dx as $dp/dx . 2h = 2 \tau.$ with h the channel halfwidth and $\tau$ the wall friction. Then obviously $v_\tau = \sqrt(\tau/\rho)$. The viscosity is chosen in function of the friction Reynolds number $Re_\tau$.

Sorry, but I still need to go over the channel case this week as Corentin suggested a slightly different Reynolds number. Do you have time to wait ?

Best,

Koen

In order to define the expression of u_tau in a periodic channel flow you need the pressure difference over the length of the channel.

You can find details in Sec.5.1 here: https://www.researchgate.net/publication/229885071_Time-accurate_intermediate_boundary_conditions_for_large_Eddy_simulations_based_on_projection_methods

Article Time-accurate intermediate boundary conditions for large Edd...