Turbulent flows at very large Reynolds numbers: new lessons learned
a P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, ul. Krasikova 23, Moscow, 117218, Russian Federation
b Lawrence Berkeley National Laboratory, Berkeley, California, USA
c University of California, Berkeley, California, USA
d National Research Nuclear University ‘MEPhI’, Kashirskoe shosse 31, Moscow, 115409, Russian Federation
The universal (Reynolds number independent) von Kármán—Prandtl logarithmic law for the velocity distribution in the basic intermediate region of turbulent shear flow is generally considered to be one of the fundamental laws of engineering science and is taught universally in fluid mechanics and hydraulics courses. In the present review it is shown that this law is based on an assumption which cannot be considered as a correct one and which does not correspond to experiment. Nor is L.D. Landau’s derivation of this law quite correct. In this paper, an alternative scaling law explicitly incorporating the influence of the Reynolds number is discussed, as well as the corresponding drag law. The study uses the concept of intermediate asymptotics and that of incomplete similarity in the similarity parameter. In the formation of these ideas Yakov Borisovich Zeldovich played an outstanding role. This work is a tribute to his glowing memory.