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We present a 3D simulation of the dynamic emergence of a twisted magneticflux tube from the top layer of the solar convection zone into the solaratmosphere and corona. It is found that after a brief initial stage of fluxemergence during which the two polarities of the bipolar region becomeseparated and the tubes intersecting the photosphere become vertical,significant rotational motion sets in within each polarity. The rotationalmotions of the two polarities are found to twist up the inner field lines ofthe emerged fields such that they change their orientation into an inverseconfiguration (i.e. pointing from the negative polarity to the positivepolarity over the neutral line). As a result, a flux rope with sigmoid-shaped,dipped core fields form in the corona, and the center of the flux rope rises inthe corona with increasing velocity as the twisting of the flux rope footpointscontinues. The rotational motion in the two polarities is a result ofpropagation of non-linear torsional Alfv\'en waves along the flux tube, whichtransports significant twist from the tube's interior portion towards itsexpanded coronal portion. This is a basic process whereby twisted flux ropesare developed in the corona with increasing twist and magnetic energy, leadingup to solar eruptions.

The Emergence of a Twisted Flux Tube into the Solar Atmosphere: Sunspot Rotations and the Formation of a Coronal Flux Rope