  We study by extensive numerical simulations the dynamics of a hard-core
tracer particle (TP) in presence of two competing types of disorder - frozen
convection flows on a square random Manhattan lattice and a crowded dynamical
environment formed by a lattice gas of mobile hard-core particles. The latter
perform lattice random walks, constrained by a single-occupancy condition of
each lattice site, and are either insensitive to random flows (model A) or
choose the jump directions as dictated by the local directionality of bonds of
the random Manhattan lattice (model B). We focus on the TP disorder-averaged
mean-squared displacement, (which shows a super-diffusive behaviour $\sim
t^{4/3}$, $t$ being time, in all the cases studied here), on higher moments of
the TP displacement, and on the probability distribution of the TP position $X$
along the $x$-axis. Our analysis evidences that in absence of the lattice gas
particles the latter has a Gaussian central part $\sim \exp(- u^2)$, where $u =
X/t^{2/3}$, and exhibits slower-than-Gaussian tails $\sim \exp(-|u|^{4/3})$ for
sufficiently large $t$ and $u$. Numerical data convincingly demonstrate that in
presence of a crowded environment the central Gaussian part and non-Gaussian
tails of the distribution persist for both models.
