An application of a recently discovered MHD instability to an open magnetic flux tube is investigated. The flux tube is gravitationally stratified and permeated by a smooth subsonic and sub-Alfvenic isothermal flow. The stability of such a tube with respect to small amplitude torsional perturbations generated at the footpoint by random convective motions is analysed. The perturbations are exponentially amplified in time if a narrow region exists where the flux tube rapidly expands. The obtained results may account for the nonthermal broadenings associated with upflows in magnetic regions of the lower solar atmosphere.