  The vertical distribution of suspended sediment concentration (SSC) remains a
subject of active research given its relevance to a plethora of problems in
hydraulics, hydrology, ecology, and water quality control. Much of the
classical theories developed over the course of 90 years represent the effects
of turbulence on suspended sediments (SS) using an effective mixing length or
eddy diffusivity without explicitly accounting for the energetics of turbulent
eddies across scales. To address this gap, the turbulent flux of sediments is
derived using a co-spectral budget (CSB) model that can be imminently used in
SS and other fine particle transport models. The CSB closes the
pressure-redistribution effect using a spectral linear Rotta scheme modified to
include isotropoziation of production and interactions between turbulent eddies
and sediment grains through a modified scale-dependent de-correlation time. The
result is a formulation similar in complexity to the widely used Rouse's
equation but with all characteristic scales, Reynolds number, and Schmidt
number effects derived from well-established spectral shapes of the vertical
velocity and accepted constants from turbulence models. Finally, the proposed
CSB model can recover Prandtl's and Rouse's equations under restricted
conditions.
