Reduced dimensional description of hydromagnetic turbulence capturing higher order fluid moments

TL;DR

This paper extends Chandrasekhar's turbulence theory to hydromagnetics by incorporating higher order fluid moments and correlation tensors, providing a more comprehensive description of energy transfer in turbulent flows.

Contribution

It introduces a novel framework that includes higher order moments and correlation tensors in turbulence modeling for hydromagnetics, enhancing the understanding of energy transfer mechanisms.

Findings

Inclusion of correlation tensors improves turbulence modeling accuracy.

Scalar representations of correlation tensors are derived for hydrodynamics and hydromagnetics.

Application to literature example shows limitations of energy spectra alone.

Abstract

In this paper, Chandrasekhar's deductive theory of turbulence is extended to the case of hydrodynamics and hydromagnetics, with higher order fluid moments. We include the contributions from correlation tensors at two different points of space and two different points in time to account for the energy transfer between Fourier modes with different $k$ values. We start with three governing equations using the first three moments of Vlasov equation, which gives us particle, momentum and energy conservation relations, respectively. We obtain the scalar representations of correlation tensors for hydrodynamics as well as hydromagnetics. Finally we pick an example from literature where the energy spectra alone was not capable of explaining the observations reported by the authors.