How Effective are the Monin–Lundgren Hierarchy and the Karman–Howarth Equation for Low-Reynolds-Number Decaying Isotropic Turbulence?

Abstract

Abstract The study of decaying homogeneous isotropic turbulence (HIT) in a series of the author's recent works is extended here to present new aspects of its nearly final period of decay and the time-dependent Loitsyanskii integral. The works contain a Gaussian family of exact solutions for a velocity probability density function (PDF) of the first equation of the Monin–Lundgren hierarchy and time-dependence of many physical quantities for a wide range of Taylor-scale Reynolds numbers (${{{\mathop{{R}}\nolimits} }_\lambda } = 40 \sim 100000$ or more). In this Letter, the case with ${{{\mathop{{R}}\nolimits} }_\lambda } = 40$ is taken up in particular, and it is revealed to be almost the lower limit for the application of our method to treat decaying HIT.