National Oceanic and
Atmospheric Administration
United States Department of Commerce


 

FY 1988

Formulas for velocity, sediment concentration and suspended sediment flux for uni-directional pressure-driven flow

Mofjeld, H.O., and J.W. Lavelle

NOAA Tech. Memo. ERL PMEL-83, NTIS: PB89-109995, 26 pp (1988)


A level 2 turbulence closure model for steady pressure-driven currents and suspended sediment concentrations in an unstratified channel leads to analytic formulas for the velocity and the concentration of each settling constituent. The level 2 model uses a parabolic form for the mixing length that increases linearly upward near the bottom and is a maximum at the surface. The model assumes a balance between local turbulence production and dissipation, and the sediment concentrations are assumed to be dilute. The level 2 velocity is found to follow closely the log velocity profile, being only 0.5u less than the log-profile at the surface, where u is the friction velocity (square root of the kinematic bottom stress). The level 2 concentration matches closely a modified form of the Rouse formula in which the actual depth H is replaced by H' = 1.07 H. The model results provide a theoretical basis for the use of the log velocity and Rouse concentration profiles over the water column based on turbulence closure theory. The vertically integrated flux of suspended sediment (suspended load transport) per unit width computed numerically from the level 2 model are approximated well by the flux derived from the pure log velocity and unmodified (H' = H) Rouse concentration profiles. When normalized by the ratio of erosion rate to the settling velocity ws, explicit formulas for the log-Rouse flux are functions of the two parameters = w/u and z/H ( being the von K rm n constant, zo the bottom roughness and H the water depth) and is most sensitive to ; it is proportional to in the slow settling regime < 0.1 and decreasing rapidly as () in the fast settling regime > 2. The flux is a strong function of the bottom stress through the erosion rate which dominates the stress dependence in the slow settling regime.




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