# [Seminar] [Applied Analysis Seminar] The Boundary of Turbulence Near the Wall?

**Speaker：Xi Chen**

**Time：10:30-11:30 Fri, March 18, 2022.**

**Zoom:**** 388 528 9728 PW: BIMSA**

**Abstract:**

The study of the ultimate statistical invariance of turbulence is a classic scientific question. Especially for the part of turbulence near the wall, which can be widely found no matter in nature or industry, to predict its asymptotic state at the limit of infinite Reynolds number will be extremely meaningful in both science and engineering because of the fact that most of the fluid’s energy will be dissipated near the wall. Prandtl proposed the classic law of wall theory one century ago and it has been very successful to predict the mean flow velocity. However, this theory doesn’t have much to say for the mean pulsating value of turbulence. From the experimental and computational data accumulated in the last six decades or so, people have found that more than 20 near-wall turbulence pulsating value( like the extremum of kinetic energy, pressure, vorticity, dissipation and many others, which we call Φ in general) will grow significantly as the Reynolds number becomes larger. To explain this fact, people generally think that maybe the relation between Φ and the Reynolds number Re is Φ∝ln(Re), which means that Re will be divergent as Φ grows and the the law of wall won’t be applicable anymore. However, in this seminar I will report a different idea developed by myself: the law-of-bounded-dissipation and universal Reynolds similarity law. In this new theory, we will have Φ∞-Φ∝Re-1/4, which means that Φ will be bounded when Re goes to infinity(see Chen & Sreenivasan, 2021 JFM; 2022 JFM). This idea has attracted lots of international attention and discussion recently(for example, ：Monkewitz 2022 JFM；Smits et al 2021 JFM；Pirozzoli et al 2021 JFM), I will also report related progress in this talk.