  We analyze the effect of the Basset history force on the sedimentation of
nearly neutrally buoyant particles, exemplified by marine snow, in a
three-dimensional turbulent flow. Particles are characterized by Stokes numbers
much smaller than unity, and still water settling velocities, measured in units
of the Kolmogorov velocity, of order one. The presence of the history force in
the Maxey-Riley equation leads to individual trajectories which differ strongly
from the dynamics of both inertial particles without this force, and ideal
settling tracers. When considering, however, a large ensemble of particles, the
statistical properties of all three dynamics become more similar. The main
effect of the history force is a rather slow, power-law type convergence to an
asymptotic settling velocity of the center of mass, which is found numerically
to be the settling velocity in still fluid. The spatial extension of the
ensemble grows diffusively after an initial ballistic growth lasting up to ca.
one large eddy turnover time. We demonstrate that the settling of the center of
mass for such light aggregates is best approximated by the settling dynamics in
still fluid found with the history force, on top of which fluctuations appear
which follow very closely those of the turbulent velocity field.
