Here are 2 interesting articles:
Cluster reveals fundamental 3-D properties of magnetic turbulence
Spectra and anisotropy of magnetic fluctuations in the Earth’s magnetosheath: Cluster observations
What the authors in second article say is, that at certain frequencies that correspond to scales roughly equal to Earth radius and SMALLER, the steepness of distribution is caused by 2D turbulence, and the break frequency (scale) coincides with possible existence of Alfven vortices- I guess 2D vortices in plasma.
What this means is that in between Earth and Sun we have a 2D/3D turbulence mix, caused by presence of Earth in the turbulent 3D solar wind plasma environment, like a defect. The presence of magnetic Earth in Solar wind kind of FILTERS out the dominance of 2D turbulence in the regions in between Earth and Sun.So I guess Sun "radiates" both 2D and 3D turbulence.
If the turbulence in magnetosheath between Earth and sun at scales smaller than Earth is mostly 2D, that of course creates and existence of an axis perpendicular to the plane of such 2D turbulence which is oriented from Sun to Earth, and naturally such orientation helps Solar excitations to path via magnetosheath by inserting energy into vortexes of such 2D turbulence. Since in 2D turbulence energy moves up, it is obvious that energy from Suns turbulent coronal magnetic movements will be moved from small scales up to higher, the highest being approximately equivalent with Earth size. Thus Earth size would be like a resonance size where 2D and 3D turbulent energy cascades meet.
If this is so, it is possible that in general Suns turbulent energy is pumped into Earth atmosphere which in turn are dissipated into Earth modes via 3D atmospheric turbulence except some stronger events that shoot through the 2D cascade without being fully cascaded up.
In general, there seems to be a coupled 2D/3D turbulence at work in magnetosheath. This resembles a behavior of a sphere/any pressurized region in turbulent flow (e.g vortex breakdown, bubbles etc) . There could be a 2D turbulence region in place where flow hits the sphere.
So there is a permanent linked turbulent cascade that starts with Sun coronal turbulence->Solar wind->Magnotosheath turbulence->Atmospheric turbulence-> and dissipates in Earth normal modes, causing Earth "hum".
Well, these are of course just conjectures.