  Evidence of surface magnetism is now observed on an increasing number of cool
stars. The detailed manner by which dynamo-generated magnetic fields giving
rise to starspots traverse the convection zone still remains unclear. Some
insight into this flux emergence mechanism has been gained by assuming bundles
of magnetic field can be represented by idealized thin flux tubes (TFTs). Weber
& Browning (2016) have recently investigated how individual flux tubes might
evolve in a 0.3 solar-mass M dwarf by effectively embedding TFTs in
time-dependent flows representative of a fully convective star. We expand upon
this work by initiating flux tubes at various depths in the upper 50-75% of the
star in order to sample the differing convective flow pattern and differential
rotation across this region. Specifically, we comment on the role of
differential rotation and time-varying flows in both the suppression and
promotion of the magnetic flux emergence process.
