Passive conserved scalar equations for PMSE

Recent experimental and theoretical work appear to support the old proposal of explaining the physical mechanism that causes Polar Mesospheric Summer Echoes (PMSE) through electron density fluctuations driven by neutral air turbulence but with a spectral inertial subrange reaching beyond the viscosity cutoff of the driving turbulence owing to the braking effect of charged dust or aerosols. In this work I generalise the work of R.J. Hill (JGR, Vol. 83, No. A3, p. 989-998, 1978) who obtained a set of coupled equations that govern the ambipolar diffusion of a three component plasma by including the effects of the neutral air turbulence which is coupled to the plasma through the stirring effect of the turbulent velocity fluctuations, in effect adding stochastic convective terms to the coupled diffusion equations. Equations of this type govern the dynamics of passive conserved scalars but only the case of one scalar has been the subject of extensive work; however no solutions in closed form are known. In the light of what is known from the theory of turbulence and passive conserved scalars, I discuss possible solutions of the set of coupled convective diffusion equations with particular applications to explaining PMSE.