Classes of hydrodynamic and magnetohydrodynamic turbulent decay

TL;DR

This paper uses numerical simulations to classify the decay behaviors of hydrodynamic and magnetohydrodynamic turbulence, revealing distinct evolutionary classes influenced mainly by physics rather than initial conditions.

Contribution

It introduces a classification scheme for turbulent decay solutions based on their trajectories in parametric plots, highlighting the physics-driven nature of these classes.

Findings

Distinct solution classes evolve along specific trajectories.

Infrared slope of initial conditions has limited influence.

Helical turbulence evolves similarly regardless of initial spectrum.

Abstract

We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k^4.