Symmetry classification of Newtonian incompressible fluid's equations flow in turbulent boundary layers

TL;DR

This paper applies Lie symmetry group methods to analyze the equations governing Newtonian incompressible fluid flow in turbulent boundary layers, deriving symmetries, solutions, and algebraic structures.

Contribution

It introduces a symmetry-based approach to solve and understand turbulent boundary layer equations, providing new invariant solutions and symmetry classifications.

Findings

Identified the symmetry group of the flow equations

Derived group-invariant solutions for turbulent boundary layers

Determined the structure of the Lie algebra of symmetries

Abstract

Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.