A convection instability characteristic of plasmas in an inhomogeneous azimuthal magnetic field is treated in the linear stage and in nonlinear saturation. The analysis is done in such a way that collisional and collisionless limits can be taken, and these limits are displayed along with the more general intermediate result. The instability, known previously in the literature in its collision‐dominated form, is shown to be a ’’flute’’ instability with collisional modifications to the growth rate. The nonlinear saturation is analyzed by examining a finite amplitude restoring‐force term in the differential equation that describes the instability. This term is due to the fact that the instability convects plasma into striations of the plasma column surface, modifying the density gradient driving force. The effects of finite ion gyroradius are displayed, and applications of this study to convection cells in a thermal plasma and to exploding wire plasmas are discussed.