High-​moment turbulent scaling laws and its roots in statistical symmetries

Vortrag von Prof. Dr. Martin Oberlack

Datum: 27.05.20  Zeit: 16.15 - 17.45  Raum: Online ZHACM

Using the symmetry-​based turbulence theory we derive turbulent scaling laws for arbitrarily high moments of the stream-​wise velocity $U_1$. In the region of the log-​law, the theory predicts an algebraic law with the exponent $t_2 (n-1)$ for moments $n > 1$. The exponent $s_2$ of the $2^{nd}$ moment determines the exponent of all higher moments. Moments here always refer to the instantaneous quantities and not to the fluctuations. For the core region of a Poiseuille flow we find a deficit law for arbitrary moments $n$ of algebraic type with a scaling exponent $n(s_2-​s_1)+2s_1-​s_2$. Hence, the moments of order one and two with its scaling exponents $s_1$ and $s_2$ determine all higher exponents. To validate the new theoretical results we have conducted a Poiseuille flow DNS at $Re_\tau=10^4$. All of the latter theoretical findings could be verified with high accuracy using DNS data.