On the emergence of very long time fluctuations and 1/f noise in ideal flows

TL;DR

This paper investigates the connection between long-time fluctuations, 1/f noise, and large-scale field reversals in ideal hydrodynamic and magnetohydrodynamic turbulence through high-precision numerical simulations, revealing their common origin.

Contribution

It uncovers the unified mechanism behind long-term phenomena in ideal turbulent flows, emphasizing the role of non-local interactions and conserved quantities.

Findings

Identification of 1/f noise in ideal turbulence spectra

Observation of delayed ergodicity and field reversals

Linking long-time fluctuations to non-local scale interactions

Abstract

This study shows the connection between three previously observed but seemingly unrelated phenomena in hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulent flows, involving the emergence of fluctuations occurring on very long time scales: the low-frequency 1/f noise in the power frequency spectrum, the delayed ergodicity of complex valued amplitude fluctuations in wavenumber space, and the spontaneous flippings or reversals of large scale fields. Direct numerical simulations of ideal MHD and HD are employed in three space dimensions, at low resolution, for long periods of time, and with high accuracy to study several cases: Different geometries, presence of rotation and/or a uniform magnetic field, and different values of the associated conserved global quantities. It is conjectured that the origin of all these long-time phenomena is rooted in the interaction of the longest wavelength fluctuations available to the system with fluctuations at much smaller scales. The strength of this non-local interaction is controlled either by the existence of conserved global quantities with a back-transfer in Fourier space, or by the presence of a slow manifold in the dynamics.