Flow instabilities of magnetic flux tubes I. Perpendicular flow

Context. The stability properties of filamentary magnetic structures are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts. Aims. In a series of papers we study the effect of external and internal flows on the stability of magnetic flux tubes. In this paper we consider the effect of a flow perpendicular to a straight, horizontal flux tube embedded in a gravitationally stratified fluid. The flow acts on the flux tube by exerting an aerodynamic drag force and by modifying the pressure stratification in the background medium. Methods. We carry out a Lagrangian linear stability analysis in the framework of the approximation of thin magnetic flux tubes. Results. The external flow can drive monotonic and oscillatory instability (overstability). The stability condition depends on direction and magnitude of the external velocity as well as on its first and second derivatives with respect to depth. The range of the flow-driven instabilities typically extends to modes with much shorter wavelengths than for the buoyancy-driven undulatory Parker instability. Conclusions. Perpendicular flows with Alfvenic Mach number of order unity can drive monotonic as well as oscillatory instability of thin magnetic flux tubes. Such instability can affect the storage of magnetic flux in stellar interiors.