Distributed chaos and inertial ranges in turbulence

TL;DR

This paper demonstrates that the emergence of an inertial range in turbulence leads to an adiabatic invariant of the energy correlation integral, resulting in a specific stretched exponential power spectrum, supported by numerical simulations.

Contribution

It reveals the connection between inertial range formation and adiabatic invariance in turbulence, providing a new understanding of the spectral form in distributed chaos.

Findings

Inertial range emergence correlates with adiabatic invariance of energy correlation.

Velocity power spectrum follows a stretched exponential form $ o \, ext{exp}(-k/k_{\beta})^{3/5}$.

Numerical simulations support the theoretical predictions.

Abstract

It is shown that appearance of inertial range of scales, adjacent to distributed chaos range, results in adiabatic invariance of an energy correlation integral for isotropic homogeneous turbulence and for buoyancy driven turbulence (with stable or unstable stratification, including Rayleigh-Taylor mixing zone). Power spectrum of velocity field for distributed chaos dominated by this adiabatic invariant has a stretched exponential form $\propto \exp(-k/k_{\beta})^{3/5}$. Results of recent direct numerical simulations have been used in order to support these conclusions.