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Existing and new direct numerical simulation (DNS) results are used to examine the effect of flow Reynolds number and pressure gradients on the law of the wall for incompressible wall-bounded turbulence. We find no evidence from DNS against the law of the wall: as the Reynolds number is increased, all sources agree precisely over an increasing range of z+ on the function U+ versus z+. This includes Couette-Poiseuille flows with mild but non-negligible, favorable and adverse, pressure gradients. We consider the law of the wall to be firmly established up to z+ ≈ 400. On the other hand, a logarithmic region (in the sense of constant logarithmic slope equal to the inverse of the von Karman coefficient κ) is not revealed for the Reynolds numbers accessible to DNS today. A constant slope roughly over the range [150,400] is recovered by introducing a shifted origin for z+, but the required value of κ is then near 0.35, which is outside the range of recent proposals, namely [0.38,0.42], let alone the range that prevailed for decades, namely [0.40,0.41].
Author(s):
Gary N Coleman
NASA
United States
Philippe R Spalart
Boeing Commercial Airplanes
United States