Intensification of the Earth's magnetic field by turbulence in the ionosphere

If the magnetic diffusivity of a fluid in turbulent motion is greater than its kinematic viscosity, then, according to Batchelor, any magnetic field initially present must ultimately decay to zero. However, if a magnetic field is externally maintained, the turbulence will generate fluctuations that may be quite large if the magnetic Reynolds number is large compared with unity. The spectrum of these fluctuations increases up to a wave number kc marking the threshold of conduction effects, and falls off rapidly beyond kc. The net effect of the turbulence can be expressed in terms of an eddy conductivity equal to the molecular conductivity multiplied by the (−5/2)th power of the magnetic Reynolds number.