One-dimensional mass transport in streams with abrupt changes in concentration at the initial site

Abstract

Problems of calculating unsteady transport of suspended sediments and dissolved admixtures in streams arise upon an abrupt increase of water turbidity near an intake structure during a flood.It is suggested that water intakes be equipped with curtain walls or regulating gates providing a steady flow in the tailwater channel.An abrupt change in the concentration of suspended sediments at the inlet to a stream leads to a redistribution of their concentration over the length and to disturbance of the dynamic equilibrium between the bottom sediments and suspended sediments.The solution of the stated problem is especially important for diversion power canals, since an increase of the sediment concentration in the forebay of penstocks leads to wear of turbine blades.For irrigation canals calculation of the distribution of the concentrations of suspended sediments over the length of the canal and in time with entry of an increased sediment concentration through the intake works is important for determining the volumes of transport to the fields together with the suspension of trace elements sorbed on them, which are necessary for plants, as well as for estimating the rate of siltation of the main and distributary canals.For canals of domestic potable or industrial water-supply systems these problems are solved for establishing the parameters of settling structures and for preventing clogging of filters.The one-dimensional equation of mass transport has the form [i, 5] (OlOt) (s~) + (o/~x) (sQ) = = O~ (O~s/dx ~)-WBS~-( 1 ) --Dz~B (Os/az) ~ ,where s is the average concentration of sediments over the cross-sectional area ~; Q is the water discharge; D x is the coefficient of dispersion in the longitudinal direction; B is the top width of the canal; ~ is the thickness of the bottom layer; D z is the vertical turbulent diffusion coefficient; W is the settling velocity.Forsteady longitudinally homogeneous transport of a suspension the relationshipholds and since (~s/~z)~ < 0, condition (i) indicates that in this case the convective flow of sediment particles suspended in water due to the settling velocity W is compensated by the diffusion flow of sediments (directed upward) due to their concentration gradient over the thickness of the "diffusion bottom layer."Within the "diffusion layer" 6 the gradient Ss~ is represented by the relationshipwhere s, = ~NV62/h is the so-called roiling turbidity [2], determined by A. V. Karaushev's formula; 8 = 5.7 x i0-~; N = MCc'g ; C C is the Chezy coefficient; M = 0.7C C + 6; V 6 is the flow velocity at height ~ (bottom velocity).We note that s, ~ does not depend on the concentration of the suspension.