The Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics

TL;DR

This paper introduces a method linking the Lagrangian frequency spectrum to turbulence interaction mechanisms, enabling differentiation between weak and strong turbulence regimes in MHD turbulence through numerical simulations.

Contribution

It establishes a relation between the Lagrangian frequency spectrum and turbulence timescales, offering a new diagnostic tool for understanding MHD turbulence dynamics.

Findings

Lagrangian spectrum relates to autocorrelation and cascade timescales.

Distinguishes weak and strong turbulence interactions.

Validated with direct numerical simulations.

Abstract

For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g. Boldyrev [Phys.Rev.Lett. \textbf{96}, 115002, 2006] and Gogoberidze [Phys.Plas. \textbf{14}, 022304, 2007], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. {A relation is found that links} the Lagrangian frequency spectrum {with} the autocorrelation timescale of the turbulent fluctuations, $\tau_\mathrm{ac}$, and the associated cascade timescale, $\tau_{\mathrm{cas}}$. Thus, the Lagrangian energy spectrum can serve to identify weak ($\tau_\mathrm{ac}\ll\tau_{\mathrm{cas}}$) and strong ($\tau_\mathrm{ac}\sim\tau_{\mathrm{cas}}$) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.