Abstract
We presently discuss newly discovered constraints that must be fulfilled by any physically reliable turbulence model. We introduce a framework that allows for the development of new models. Heavy use is made of the mathematical concept of Lie symmetries, which provides an algorithmic way of extracting important physical properties of any given system of governing equations. The analysis presented here unifies, generalizes and extends concepts such as dimensional analysis and tensor invariant modeling, which in the past has been used extensively for turbulence modeling purposes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.duP. Donaldson, H. Rosenbaum, Calculation of the turbulent shear flows through closure of the Reynolds equations by invariant modeling. Aeronaut. Res. Assoc. Princeton (127) (1968)
M. Oberlack, A. Rosteck, New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws. Discret. Contin. Dyn. Syst. Ser. S 3(3) (2010)
O. Reynolds, On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. R. Soc. Lond. A 186, 123–164 (1895)
A. Rosteck, M. Oberlack, Lie algebra of the symmetries of the multi-point equations in statistical turbulence. J. Nonlinear Math. Phys. 18(1) (2011)
H. Sadeghi, M. Oberlack, M. Gauding, On new scaling laws in a temporally evolving turbulent plane jet using lie symmetry analysis and direct numerical simulation. J. Fluid Mech. (2018)
M. Waclawczyk, N. Staffolani, M. Oberlack, A. Rosteck, M. Wilczek, R. Friedrich, Statistical symmetries of the Lundgren-Monin-Novikov hierarchy. Phys. Rev. 90, 1–11 (2014)
Acknowledgements
The work of Dario Klingenberg is supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at Technical University Darmstadt.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Klingenberg, D., Oberlack, M., Pluemacher, D. (2019). Symmetry-Based Turbulence Modeling. In: Örlü, R., Talamelli, A., Peinke, J., Oberlack, M. (eds) Progress in Turbulence VIII. iTi 2018. Springer Proceedings in Physics, vol 226. Springer, Cham. https://doi.org/10.1007/978-3-030-22196-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-22196-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-22195-9
Online ISBN: 978-3-030-22196-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)