r_max, calculated from Eq. (5), as a function of Mach number ℳ. Top left: resolution study for k = 8. Top right to bottom left (clockwise): simulations with k = 8, k = 16, and k = 4 respectively, all with resolution 0.16 pc and different turbulent seeds shown as different colours. The two horizontal dotted lines indicates the size of the box (40 pc) and the fiducial resolution (0.16 pc). The values obtained for high ℳ are unreasonably high, meaning that the force experienced by a BH in a turbulent medium is not well approximated by the analytic formalism developed for a homogeneous medium.