Stationary and non-stationary energy cascades in homogeneous ferrofluid turbulence

TL;DR

This paper derives an exact relation for energy transfer in turbulent ferrofluids, validating it through simulations for both stationary and non-stationary regimes, revealing different cascade behaviors under varying magnetic fields.

Contribution

The study introduces an exact relation for energy transfer in ferrofluid turbulence and validates it with simulations, highlighting differences between stationary and non-stationary cascades.

Findings

Kinetic and total energy cascade rates are nearly equal under weak magnetic fields.

Stationary cascade regime shows good agreement between transfer rate and energy injection.

Strong magnetic fields induce non-stationary turbulence with different cascade rates for kinetic and total energy.

Abstract

The nonlinear transfer rate of the total energy (transfer rate of kinetic energy + transfer rate due to the work done by the magnetization) for an incompressible turbulent ferrofluid system is studied under the assumption of statistical homogeneity. Using the formalism of the two-point correlators, an exact relation connecting the second-order statistical moments to the average energy injection rate is derived for the scale-to scale transfer of the total energy. We validate the universality of the exact relation through direct numerical simulations for stationary and non-stationary cascade regimes. For a weak external magnetic field, both kinetic and the total energy cascade with nearly the same cascade rate. A stationary cascade regime is achieved and hence a good agreement between the exact energy transfer rate and the average energy injection is found. Due to the rapid alignment of the ferrofluid particles in the presence of strong external fields, the turbulence dynamics becomes non-stationary. Interestingly, there too, both kinetic and the total energy exhibit inertial range cascades but with different cascade rates which can be explained using the non-stationary form of our derived exact relation.