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Martin Oberlack
Chair of Fluid Dynamics, Dept. Mech. Eng., TU Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany; Center of Smart Interfaces, TU Darmstadt, Germany; GS Computational Engineering, TU Darmstadt, Germany

Holger Wenzel
Institut for Mechanics, RWTH Aachen 52056 Aachen, Germany

Norbert Peters
Department of Combustion Technology RWTH Aachen University Templergraben 64, 52056 Aachen, Germany


It is demonstrated that the G-equation for premixed combustion admits a diversity of symmetries properties, i.e. invariance characteristics under certain transformations. Included are those of classical mechanics such as Galilean invariance, rotation invariance and others. Also a new generalized scaling symmetry has been established. It is shown that the generalized scaling symmetry precisely defines the physical property of the G-equation. That is to say the value of G at a given flame front is arbitrary. It is also proven that the generalized scaling symmetry precludes the application of classical Reynolds ensemble averaging usually employed in statistical turbulence theory in order to avoid non-unique statistical quantities such as for the mean flame position. Finally a new averaging scheme of the G-field is presented being fully consistent with all symmetries of the G-equation.