Spatio-Temporal Energy Cascade in Three-Dimensional Magnetohydrodynamic Plasma Turbulence

The very defining property of plasma turbulence is its ability to produce fluctuations with broadband wavenumber and frequency energy spectra. Spacecraft observations in the solar wind (SW) have revealed that turbulent fluctuations have nontrivial temporal properties, with a tendency for energy to accumulate in low frequency modes, a behavior that has also been observed in numerical simulations. However, the physical origin of such low frequency fluctuations is still debate, and it is not clear whether low frequency modes play a significant role in driving the turbulent cascade, or if they are dynamically irrelevant.

In our work, we present an extension of the coarse grained (CG) magnetohydrodynamics (MHD) equations to investigate plasma turbulence in wavenumber-frequency space. Our method allows to track the transfer of turbulent energy among fluctuations with different spatio-temporal scales. Using 3D MHD simulations of SW turbulence, we use our extended CG approach to study the origin of low frequency modes, and their contribution to the turbulent cascade. We show that magnetic energy exhibits an inverse cascade toward small wavenumbers and frequencies. Low frequency magnetic fluctuations support the turbulent cascade by acting as an energy reservoir that is converted into plasma kinetic energy. Finally, the fluid kinetic energy undergoes a direct cascade toward high wavenumbers and frequencies, where energy is ultimately dissipated. Our results provide a new framework to study the spatio-temporal properties of turbulence.