  A numerical model is presented to describe both the transient and
steady-state dynamics of viscous threads falling onto a plane. The steady-state
coiling frequency w is calculated as a function of fall height H. In the case
of weak gravity, w ~ H^{-1} and w ~ H are obtained for lower and higher fall
heights respectively. When the effect of gravity is significant, the relation w
~ H^2 is observed. These results agree with the scaling laws previously
predicted. The critical Reynolds number for coil-uncoil transition is
discussed. When the gravity is weak, the transition occurs with hysteresis
effects. If the plane moves horizontally at a constant speed, a variety of
meandering oscillation modes can be observed experimentally. The present model
also can describe this phenomenon. The numerically obtained state diagram for
the meandering modes qualitatively agrees with the experiment.
