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<br />Sediment transport, in the presence of transverse flow, has a component <br />in that direction. Sediment movement in the transverse direction contribu- <br />tes to the adjustment of transverse bed profile. In an unsteady flow, the <br />transverse bed profile varies with time, and it is constantly adjusted <br />toward equilibrium through scour and deposition. The transverse bed load <br />per unit channel length %' can be related to the streamwise transport %. <br />Such a relationship by Ikeda (1982) can be written in parametric fOIll1 as <br /> <br />'3b' ~ dZ) <br />-=F tan$,-- <br />'3b tJ r <br /> <br />(14) <br /> <br />where S is the angle of deviation of bottom currents from the streamwise <br />direction. The near-bed transverse velocity is a function of the curvature, <br />and it is canputed using the flow curvature. <br /> <br />Eq. 14 relates the direction of bed-load movement to the direction of <br />near-bed velocity and transverse bed slope dz/3r. As transverse velocity <br />starts to move sediment away from the concave bank, it creates a transverse <br />bed slope that counters the transverse sediment movement. An equilibrium is <br />reached, i.e., '3b' = 0, when the effects of these opposing tendencies are in <br />balance. Transverse bed-profile evolution is related to the variation in <br />bed-material load. Ikeda and Nishmura (1986) developed a method for <br />estimating transport and diffusion of fine sediments in the transverse <br />direction by vertical integration of suspended load over the depth. Their <br />model for predicting the transverse bed slope is also employed. <br /> <br />Changes in channel-bed elevation at a point due to transverse sediment <br />movement are comJ;Uted using the transverse continui ty equation for sediment <br /> <br />dZ <br />)t <br /> <br />1 1 d <br />+------ <br />1 - 11. r (Jr <br /> <br />(r lls') = 0 <br /> <br />(15) <br /> <br />written in finite difference form with a forward difference for qs', this <br />equation becomes <br /> <br />c.t <br />L::,.zk = ----- <br />1-). <br /> <br />r q' r q' <br />2 ~:t!_~~:!:1_=__~__~~ <br />rk rk+l - I:k-l <br /> <br />(16) <br /> <br />where k is the radial (transverse) coordinate index measured from the center <br /> <br />21 <br />