### Mathematics Colloquium

# Martin Oberlack

### (TU Darmstadt)

## "What can Lie-symmetry groups teach us on turbulence statistics?"

** Date: ** |
Wed, April 8, 2015 |

** Time: ** |
17:15 |

** Place: ** |
Research II Lecture Hall |

**Abstract:** Text-book knowledge proclaims that Lie symmetries such as Galilean
transformation lie at the heart of fluid dynamics. These important properties
also carry over to the statistical description of turbulence, i.e. to the
Reynolds stress transport equations and its generalization, the multi-point
correlation equations (MPCE). Interesting enough, the MPCE admit a much larger
set of symmetries, in fact infinite dimensional, subsequently named
statistical symmetries.

Most important, theses new symmetries have important consequences for our
understanding of turbulent scaling laws. The symmetries form the essential
foundation to construct exact solutions to the infinite set of MPCE, which in
turn are identified as classical and new turbulent scaling laws. Examples on
various classical and new shear flow scaling laws including higher order
moments will be presented. Even new scaling have been forecasted from these
symmetries and in turn validated by DNS.

Turbulence modellers have implicitly recognized at least one of the
statistical symmetries as this is the basis for the usual log-law which has
been employed for calibrating essentially all engineering turbulence models.
An obvious conclusion is to generally make turbulence models consistent with
the new statistical symmetries.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*