  In this paper we seek to understand the timescale on which the photospheric
motions on the Sun braid coronal magnetic field lines. This is a crucial
ingredient for determining the viability of the braiding mechanism for
explaining the high temperatures observed in the corona. We study the
topological complexity induced in the coronal magnetic field, primarily using
plasma motions extracted from magneto-convection simulations. This topological
complexity is quantified using the field line winding, finite time topological
entropy and passive scalar mixing. With these measures we contrast mixing
efficiencies of the magneto-convection simulation, a benchmark flow known as a
``blinking vortex', and finally photospheric flows inferred from sequences of
observed magnetograms using local correlation tracking. While the highly
resolved magneto-convection simulations induce a strong degree of field line
winding and finite time topological entropy, the values obtained from the
observations from the plage region are around an order of magnitude smaller.
This behavior is carried over to the finite time topological entropy.
Nevertheless, the results suggest that the photospheric motions induce complex
tangling of the coronal field on a timescale of hours.
