  To understand how spatiotemporal chaos may modify material transport, we use
direct numerical simulations of the three-dimensional Boussinesq equations and
of an advection-diffusion equation to study the transport of a passive tracer
by the spiral defect chaos state of a convecting fluid. The simulations show
that the transport is diffusive and is enhanced by the spatiotemporal chaos.
The enhancement in tracer diffusivity follows two regimes. For large Peclet
numbers (that is, small molecular diffusivities of the tracer), we find that
the enhancement is proportional to the Peclet number. For small Peclet numbers,
the enhancement is proportional to the square root of the Peclet number. We
explain the presence of these two regimes in terms of how the local transport
depends on the local wave numbers of the convection rolls. For large Peclet
numbers, we further find that defects cause the tracer diffusivity to be
enhanced locally in the direction orthogonal to the local wave vector but
suppressed in the direction of the local wave vector.
