  One of the physically least understood characteristics of geophysical
transport of sediments along sediment surfaces is the well known experimental
observation that the sediment transport rate $Q$ is linearly dependent on the
fluid shear stress $\tau$ applied onto the surface in air, but is nonlinearly
dependent on $\tau$ in water. Using transport simulations for a wide range of
driving conditions, we show that the scaling depends on the manner in which the
kinetic fluctuation energy of transported particles is dissipated: via
predominantly fluid drag and quasistatic contacts (linear) versus fluid drag
and quasistatic and collisional contacts (nonlinear). We use this finding to
derive a scaling law (asymptotically $Q\sim\tau^2$) in simultaneous agreement
with measurements in water and air streams.
