  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.
