Bottlenecks in turbulent kinetic energy spectra predicted from structure function inflections using the Von Kármán-Howarth equation

Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Sep;92(3):033009. doi: 10.1103/PhysRevE.92.033009. Epub 2015 Sep 11.

Abstract

The compensated three-dimensional turbulent kinetic energy spectrum exhibits a peculiar bump at wave numbers in the vicinity of the crossover from inertial to viscous regimes due to pile up in turbulent kinetic energy, a phenomenon referred to as the bottleneck effect. The origin of this bump is linked to an inflection point in the second-order structure function in physical space caused by competition between vortex stretching and viscous diffusion mechanisms. The bump location and magnitude are reasonably predicted from a novel analytical solution to the Von Kármán-Howarth equation reflecting the competition between these two mechanisms and accounting for variable structure skewness with decreasing scale.