The calculation of turbulence statistics is considered the key unsolved problem of fluid
mechanics, ie, precisely the computation of arbitrary statistical velocity moments from first …

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

We present new scaling expressions, including high-Reynolds-number ($ Re $) predictions,
for all Reynolds stress components in the entire flow domain of turbulent channel and pipe …

First-principle-based prediction of mean-flow quantities of wall-bounded turbulent flows
(channel, pipe and turbulent boundary layer (TBL)) is of great importance from both physics …

A fully developed, turbulent Poiseuille flow with wall transpiration, ie uniform blowing and
suction on the lower and upper walls correspondingly, is investigated by both direct …

A critical review is presented on the most recent attempt to generally explain the notion of"
statistical symmetry". This particular explanation, however, is incomplete and misses one …

The present paper shows that local similarity theories, proposed for the strongly-stratified
boundary layers, can be derived as invariant solutions defined under the Lie-group theory. A …

The symmetry-based turbulence theory has been used to derive new scaling laws for the
streamwise velocity and temperature moments of arbitrary order. For this, it has been …

Despite dedicated effort for many decades, statistical description of highly technologically
important wall turbulence remains a great challenge. Current models are unfortunately …

This work applies new insights into turbulent statistics gained by Lie symmetry analysis to
the closure problem of turbulence. Founded in the mathematics of partial differential …