This study investigates the stability of a model siphon flow along a thin magnetic flux tube embedded in an isothermal medium. The behaviour of models with flow speeds about equal to the tube-speed is considered. Three kinds of flow are dealt with: purely subcritical; transcritical; and purely supercritical. A simple stationary equilibrium model of a siphon flow along a solar penumbral filament is constructed. Ideal magnetohydrodynamics and the approximation of thin flux tubes are applied. The adiabatic equation serves as energy equation. In case of transcritical flow, generalized Hugoniot conditions (Herbold et al., 1985) are satified across a shock in the downstream leg of the flow. The location of the shock is determined by the choice of one physical quantity, e.g. the density, at the downstream footprint. The linear formalism derived by Schmitt (1998) is applied to study the stability of the equilibirum model. Purely subcritical flows turn out to be stable whereas purely suppercritical ones are unstable. The transcritical ones require special treatment at the critical points where the stability equations become singular. Application of regularity conditions suggests instability for transcritical flow, but the boundary conditions need to be adjusted to get any solutions at all. As an alternative, the stability of the transcritical flow without a shock is studied without the application of regularity conditions. This approach shows that instability occurs at the critical point.
