The Lie group approach developed by Oberlack (1997) is used to
derive new scaling
laws for high-Reynolds-number turbulent pipe flows. The scaling laws, or,
methodology of Lie groups, the invariant solutions, are based on the mean
fluctuation momentum equations. For their derivation no assumptions other
similarity of the Navier–Stokes equations have been introduced where
decomposition into the mean and fluctuation quantities has been implemented.
set of solutions for the axial mean velocity includes a logarithmic scaling
is distinct from the usual law of the wall, and an algebraic scaling law.
an algebraic scaling law for the azimuthal mean velocity is obtained. In
laws the origin of the independent coordinate is located on the pipe axis,
in contrast to the usual wall-based scaling laws. The present scaling laws
agreement with both experimental and DNS data. As observed in experiments,
shown that the axial mean velocity normalized with the mean bulk velocity
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