Propagation of nonlinear longitudinal-transverse waves along magnetic flux tubes in the solar atmosphere III. Modified equation of motion

In this series of papers the time-dependent propagation of nonlinear longitudinal-transverse waves in thin vertical magnetic flux tubes embedded in the solar atmosphere is investigated numerically using the (one-dimensional) thin tube approximation. As in the last decade the particular form of the backreaction term in the transverse equation of motion has been under considerable dispute we investigate this issue once again and suggest a new expression for the backreaction term in the local approximation. This new expression intends to avoid criticisms leveled at the previous terms. In the present paper we numerically compare the actual effects these different terms produce in a number of cases including the situations where the reported discrepancies are prominent. We find that noticeable discrepancies between the various proposed backreaction terms occur only, when strong longitudinal fluid flows are present simultaneously with the swaying of the tube and that for weak flows these discrepancies disappear. If only weak longitudinal flows occur it thus appears that the particular choice of the backreaction term is not important.