Convective turbulence in weakly ionized plasma

We show that the two-dimensional E x B and Rayleigh-Taylor driven turbulence in the weakly ionized plasma of the Earth's ionosphere is isomorphic to the viscous convection of an ordinary fluid in a porous medium due to temperature gradients (E is the ambient electric field and B is the magnetic field). The turbulence results in fluctuations of the electron density which have been observed for several decades by incoherent radar backscattering techniques and rocket mounted instruments. A two-dimensional single field equation has been derived to describe this convective turbulence. Numerical simulations of this equation reveal a strong anisotropy in the turbulence, which consists of rising hot bubbles and falling cool bubbles. These bubbles break up into fingers. Sharp gradients are generated in the direction perpendicular to gravity or equivalently the driving electric field E. After reaching a quasisteady state, the omnidirectional energy spectrum approaches k^-2. Physical mechanisms leading to anisotropy are analysed. An equation, analogous to that for the convective ionospheric plasma, but applicable instead to the two-dimensional convection in the Earth's mantle is derived and simulated. The results from this simulation are discussed.