  High $p_T > 10$ GeV elliptic flow, which is experimentally measured via the
correlation between soft and hard hadrons, receives competing contributions
from event-by-event fluctuations of the low $p_T$ elliptic flow and event plane
angle fluctuations in the soft sector. In this paper, a proper account of these
event-by-event fluctuations in the soft sector, modeled via viscous
hydrodynamics, is combined with a jet energy loss model to reveal that the
positive contribution from low $p_T$ $v_2$ fluctuations overwhelms the negative
contributions from event plane fluctuations. This leads to an enhancement of
high $p_T > 10$ GeV elliptic flow in comparison to previous calculations and
provides a natural solution to the decade long high $p_T$ $R_{AA} \otimes v_2$
puzzle. We also present the first theoretical calculation of high $p_T$ $v_3$,
which is shown to be compatible with current LHC data. Furthermore, we discuss
how short wavelength jet-medium physics can be deconvoluted from the physics of
soft, bulk event-by-event flow observables using event shape engineering
techniques.
