In this work, the known analogy between the convection instability of a normal liquid and one of the most dangerous forms of plasma instability in a magnetic field – the so-called convective, or commutation instability is extended to include the non-linear flows arising as a consequence of instability. In the first section, the turbulent convection of a plasma in traps with magnetic mirrors and in a discharge, with a longitudinal field of moderate strength, is examined. An explanation is furnished in this way of a mtmber of peculiarities in the behaviour of a plasma in experimental devices of this type. The second section deals with convection arising in a plasma in the presence of a longitudinal current. It is shown, that on the basis of the current convection mechanism, it is possible to explain the anomalous,diffusion of plasma in a positive column.