A computer model for meandering rivers with multiple bed load sediment sizes 1. Theory

A computer model for meandering rivers that couples water flow, bed topogra phy, the sorting of sediments with different grain sizes, and channel migra tion has been developed using the linear theory of Johannesson and Parker [ 1989] for the dynamics of meandering rivers and the theory of Parker and An drews [1985] for bed load sediment transport and sorting in meander bends. The equations for single-size sediment transport used in the linear theory of Johannesson and Parker were replaced by multiple-size sediment transport and sorting equations obtained from the theory of Parker and Andrews. This paper is the first of a pair. In this paper, the theoretical framework of the model is presented, and the derivation of the theory from the earlier t heories is detailed. It is shown that there are five different regions in t he two-dimensional model parameter space [epsilon (G(1) - 3), (pi /2)(2)G(2 )], where G(1) is a measure of the coupling of the longitudinal sediment fl ow to the longitudinal water flow, epsilon is the resealed bed friction coe fficient, and G(2) characterizes the coupling of the transverse (cross chan nel) sediment flow to the transverse component of the bed inclination. The model is not stable in two of the regions (regions I and 2). Alternating ba rs develop in region 4 but propagate along the channel with damped amplitud es, and no alternating bars develop in region 5. In region 3, which is the boundary between regions 2 and 4, alternating bars develop and propagate un damped throughout the entire channel. Increasing the floodplain inclination , channel width/depth ratio, average sediment size, or the breadth of the s ediment size distribution in the model increases the tendency toward a tran sition from a stable meandering state to an unstable, presumably braided, s tate.