  Analogue gravity models describe linear fluctuations of fluids as a massless
scalar field propagating on stationary acoustic spacetimes constructed from the
background flow. In this paper, we establish that this paradigm generalizes to
arbitrary order nonlinear perturbations propagating on dynamical analogue
spacetimes. Our results hold for all inviscid, spherically symmetric and
barotropic non-relativistic flows in the presence of an external conservative
force. We demonstrate that such fluids always admit a dynamical description
governed by a coupled pair of wave and continuity equations. We provide an
iterative approach to solve these equations about any known stationary solution
to all orders in perturbation. In the process, we reveal that there exists a
dynamical acoustic spacetime on which fluctuations of the mass accretion rate
propagate. The dynamical acoustic spacetime is shown to have a well defined
causal structure and curvature. In addition, we find a classical fluctuation
relation for the acoustic horizon of the spacetime that admit scenarios wherein
the horizon can grow as well as recede, with the latter being a result with no
known analogue in black holes. As an example, we numerically investigate the
Bondi flow accreting solution subject to exponentially damped time dependent
perturbations. We find that second and higher order classical perturbations
possess an acoustic horizon that oscillates and changes to a new stable size at
late times. In particular, the case of a receding acoustic horizon is realized
through `low frequency' perturbations. We discuss our results in the context of
more general analogue models and its potential implications on astrophysical
accretion flows.
