Determination of energy flux rate in homogeneous ferrohydrodynamic turbulence using two-point statistics

Under the influence of an external magnetic field H, the suspended ferromagnetic particles of a laminar ferrofluid flow try to be oriented along H through a relaxation mechanism. Turbulence affects the interaction between the magnetization of each suspended particle and the external field thereby leading to a large relaxation time and hence a slow relaxation process. This can be obtained by replacing viscous drag force with turbulent drag force in Brownian motion. We show that the total energy is an inviscid invariant in turbulent ferrofluids. Using two-point statistics we formulate an exact relation in the inertial zone of incompressible ferrofluid turbulence. This exact relation gives an accurate measure of the energy dissipation rate in a turbulent ferrofluid. We also show that $(\mathbf{u}\times \mathit{\omega }), (\mathbf{M}\times \mathbf{H}), (\mathbf{M}·\mathbf{\nabla })\mathbf{H}$, and $(\mathit{\omega }\times \mathbf{M})$ play the major role in energy cascading in turbulent ferrofluids.