Universal mechanism for saturation of vorticity growth in fully developed fluid turbulence

Abstract

AbstractNumerical results from large-scale, long-time, simulations of decaying homogeneous turbulence are reported, which indicate that blow-up of inviscid flows is tamed by the emergence of collective dynamics of coherent structures. The simulations also suggest that this collective dynamics might lead to universal behaviour during the transient evolution of turbulence. In particular, simulations with three different initial conditions show evidence of a ${k}^{- 3} \log k$ spectrum in the transient stage, before the Kolmogorov ${k}^{- 5/ 3} $ asymptotic regime is attained. Such a universal transient might serve as a spectral funnel to the time-asymptotic Kolmogorov spectrum, which is invariably observed in the late stage of all three simulations presented in this work. The present work is entirely based on simulation evidence. However, the statistical analysis of the coherent structures suggests an analogy with population dynamics, which might be conducive to new mathematical models of transient decaying turbulence.