  Sub-stellar objects exhibit photometric variability, which is believed to be
caused by a number of processes, such as magnetically-driven spots or
inhomogeneous cloud coverage. Recent models have shown that turbulent flows and
waves, including internal gravity waves, may play an important role in cloud
evolution.
  The aim of this paper is to investigate the effect of IGW on dust nucleation
and dust growth, and whether observations of the resulting cloud structures
could be used to recover atmospheric density information.
  For a simplified atmosphere in two dimensions, we numerically solved the
governing fluid equations to simulate the effect on dust nucleation and mantle
growth as a result of the passage of an IGW. Furthermore, we derived an
expression that relates the properties of the wave-induced cloud structures to
observable parameters in order to deduce the atmospheric density.
  Numerical simulations show that the $\rho, p, T$ variations caused by gravity
waves lead to an increase of the nucleation rate by up to a factor 20, and an
increase of the mantle growth rate by up to a factor 1.6, compared to their
equilibrium values. An exploration of the wider parameter space shows that in
absolute terms, the increase in nucleation due to IGW is stronger in cooler (T
dwarfs) and TiO2-rich sub-stellar atmospheres. The relative increase, however,
is greater in warmer (L dwarf) and TiO2-poor atmospheres due to conditions less
suited for efficient nucleation at equilibrium. These variations lead to banded
areas in which dust formation is much more pronounced, similar to the cloud
structures observed on Earth.
  We show that IGW in the atmosphere of sub-stellar objects can produce banded
clouds structures similar to that observed on Earth. We propose a method with
which potential observations of banded clouds could be used to estimate the
atmospheric density of sub-stellar objects.
