The characteristics of motion of thin magnetic tubes

Starting from the equations of motion of a thin magnetic tube, the characteristic curves and velocities and compatibility relations are derived as basis for investigating its motion and for correctly formulating the problem of stationary solution. It is shown that the characteristic velocity of transverse waves is related to the Alfvén Mach number of the flow in the tube. When the flow velocity exceeds the critical value for the Kelvin-Helmholtz instability, transverse waves cease to exist.