Turbulent Poiseuille Flow with Wall Transpiration: Analytical Study and Direct Numerical Simulation

We present an analytical and direct numerical simulation (DNS) study to describe an incompressible, fully developed turbulent Poiseuille flow with wall transpiration i.e. uniform transverse velocity with constant flux on the wall. The DNS was conducted at Re-tau = 250 for different relative transpiration velocities. The DNS data serve as a first test case of a new turbulent scaling law in the form of a logarithm. DNS data validates the new turbulent logarithmic scaling law derived from Lie symmetry theory of the infinite dimensional multi-point correlation equation and is principally different from the classical near-wall log-law. We will show that the DNS data agree with the new turbulent scaling law over practically the whole cross-section of the channel.