This paper is concerned with a review of models of ionospheric plasma. Two hierarchies of models are presented, both of them leading to the so-called striation model. A linear stability analysis is performed and shows that the striation model can developed plasma instabilities. A dissipation process has disappeared during the limiting process. In order to add a dissipation mechanism to the striation model, we propose to use a statistical approach to turbulence and derive a so-called ’turbulent striation model’. Numerical simulations are proposed to show the gain of stability.