  We show that in a turbulent flow transporting suspended sediment, the
unsaturated sediment flux $q(x,t)$ can be described by a first-order relaxation
equation. From a mode analysis of the advection-diffusion equation for the
particle concentration, the relaxation length and time scales of the dominant
mode are shown to be the deposition length $H U/V_{\rm fall}$ and deposition
time $H/V_{\rm fall}$, where $H$ is the flow depth, $U$ the mean flow velocity
and $V_{\rm fall}$ the sediment settling velocity. This result is expected to
be particularly relevant for the case of sediment transport in slowly varying
flows, where the flux is never far from saturation. Predictions are shown to be
in quantitative agreement with flume experiments, for both net erosion and net
deposition situations.
