Third-order anomaly and the Zeroth Law of turbulence

A building block of any turbulence theory is that the mean kinetic energy dissipation rate is finite in the inviscid limit – known as the Zeroth Law of turbulence. In homogeneous and isotropic turbulence, this has been tested many times, both experimentally and computationally. Yet, since one cannot prove this result by data alone, several theoretical efforts have been made to put it on a firm ground. Such efforts are of fundamental importance. One of them is based on the relation between the mean energy dissipation rate and the scaling of the third-order absolute velocity increment. We will explore this relation in this talk using data from experiments and simulations of homogeneous and isotropic turbulence.