  Results from Juno's microwave radiometer indicate non-uniform mixing of
ammonia vapor in Jupiter's atmosphere down to tens of bars, far beneath the
cloud level. Helioseismic observations suggest solar convection may require
narrow, concentrated downdrafts called entropy rain to accommodate the Sun's
luminosity. Both observations suggest some mechanism of non-local convective
transport. We seek to predict the depth that a concentrated density anomaly can
reach before efficiently mixing with its environment in bottomless atmospheres.
We modify classic self-similar analytical models of entraining thermals to
account for the compressibility of an abyssal atmosphere. We compare these
models to the output of high resolution three dimensional fluid dynamical
simulations to more accurately model the chaotic influence of turbulence. We
find that localized density anomalies propagate down to ~3-8 times their
initial size without substantially mixing with their environment. Our analytic
model accurately predicts the initial flow, but the self-similarity assumption
breaks down after the flow becomes unstable at a characteristic penetration
depth. In the context of Jupiter, our findings suggest that precipitation
concentrated into localized downdrafts of size ~20km can coherently penetrate
to on the order of a hundred kilometers (tens of bars) beneath its initial
vaporization level without mixing with its environment. This finding is
consistent with expected convective storm length-scales, and Juno MWR
measurements of ammonia depletion. Compositional gradients of volatiles beneath
their cloud levels may be common on stormy giant planets. In the context of the
Sun, we find that turbulent downdrafts in abyssal atmospheres cannot maintain
their coherence through the Sun's convective layer, a potential challenge for
the entropy rain hypothesis.
