Amplification of magnetic field twisting by a stagnation point flow

Context. Flows are a common feature of many processes occurring in the solar atmosphere, such as the formation of prominences where evaporated plasma from the chromosphere condensates along thin prominence threads that are seen to twist and oscillate. Aim. We aim to investigate the twisting of these threads by plasma condensation during their formation. Methods. We introduce a simple model with fixed critical points where the flow speed matches the Alfvén speed. This allows us to study the problem separately in the sub-Alfvénic and super-Alfvénic regimes. The temporal and spatial evolution of small amplitude initial twists along a thread is investigated analytically and numerically. Results. Analytical solutions are constructed in terms of the generalised hypergeometric functions. The solutions grow in time, despite the absence of any influxes of energy or magnetic fields. These results are confirmed numerically: We find oscillations with an amplifying amplitude and increasing period in the sub-Alfvénic regime. In the super-Alfvénic regime, we find twist amplification without any accompanying oscillations. An interesting result is the convergence of the twists at the critical points that leads to the formation of steep gradients and small scales. Energy is transferred from the flow to the amplifying twists. Conclusions. Magnetic field lines may be twisted by a stagnation point flow without the influx of any azimuthal field or energy. This twisting could assist in the formation of topology that is able to support the growth of prominences. The formation of steep gradients and small scales at the critical point is a new phenomenon which requires further investigation in the non-linear regime with the inclusion of magnetic diffusion.