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The asymptotic energy dissipation is connected to the third-order scaling ofthe longitudinal velocity increment magnitude in three-dimensional turbulencevia the Kolmogorov $4/5$ law. It is shown that the third-order longitudinalabsolute velocity increment scaling should not exceed unity for anomalousdissipation to occur, that is for non-vanishing average dissipation in theinviscid limit -- also known as the ``zeroth law" of turbulence. Conversely, ifthe third-order longitudinal absolute velocity increment scaling exceeds unitythen the average dissipation must asymptotically vanish and the velocityincrement field will becomes symmetric at least at the level of its skewness.This work highlights the importance of the third-order absolute velocityincrement scaling in assessing the status of the ``zeroth-law" of turbulence.

Dependence of the asymptotic energy dissipation on third-order velocity scaling