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

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 …

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 …

The present article is intended to give a broad overview and present details on the Lie
symmetry induced statistical turbulence theory put forward by the authors and various other …

A recent Letter by Oberlack et al.[Phys. Rev. Lett. 128, 024502 (2022)] claims to have
derived new symmetry-induced solutions of the non-modelled statistical Navier-Stokes …

The problem of turbulence statistics described by the Lundgren–Monin–Novikov (LMN)
hierarchy of integro-differential equations is studied in terms of its group properties. For this …

In the present work, the problem of RANS (Reynolds-Averaged Navier–Stokes) turbulence
modeling is investigated from a novel angle by considering recently discovered constraints …

The Lie-group-based symmetry analysis, as first proposed in Avsarkisov et al.(2014) and
then later modified in Oberlack et al.(2015), to generate invariant solutions in order to predict …

The scale invariance of geophysical fluids is investigated in terms of a scale invariance
criterion. It was developed by Schaefer-Rolffs et al.(2015) based on the implication that each …