Abstract
The transport of sediment by a fluid along the surface is responsible
for dune formation, dust entrainment, and a rich diversity of patterns
on the bottom of oceans, rivers, and planetary surfaces. Most previous
models of sediment transport have focused on the equilibrium (or
saturated) particle flux. However, the morphodynamics of sediment
landscapes emerging due to surface transport of sediment is controlled
by situations out of equilibrium. In particular, it is controlled by the
saturation length characterizing the distance it takes for the particle
flux to reach a new equilibrium after a change in flow conditions. The
saturation of mass density of particles entrained into transport and the
relaxation of particle and fluid velocities constitute the main relevant
relaxation mechanisms leading to saturation of the sediment flux. Here
we present a theoretical model for sediment transport which, for the
first time, accounts for both these relaxation mechanisms and for the
different types of sediment entrainment prevailing under different
environmental conditions. Our analytical treatment allows us to derive a
closed expression for the saturation length of sediment flux, which is
general and thus can be applied under different physical conditions.
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