Flow instabilities of magnetic flux tubes IV. Flux storage in the solar overshoot region

We consider the effects of material flows on the dynamics of toroidal magnetic flux tubes located close to the base of the solar convection zone, initially within the overshoot region. The problem is to find the physical conditions in which magnetic flux can be stored for periods comparable to the dynamo amplification time, which is of the order of a few years. We carry out nonlinear numerical simulations to investigate the stability and dynamics of thin flux tubes subject to perpendicular and longitudinal flows. We compare the simulations with the results of simplified analytical approximations. We determine ranges of the flow parameters for which a linearly Parker-stable magnetic flux tube is stored in the middle of the overshoot region for a period comparable to the dynamo amplification time. The residence time for magnetic flux tubes with fluxes of 2x10^{21} Mx in the convective overshoot layer is comparable to the dynamo amplification time, provided that the average speed and the duration of the downflow do not exceed about 50 m/s and 100 days, respectively, and that the lateral extension of the flow is smaller than about 10 degrees.