Reformulation of the bed load equation of Meyer‐Peter and Müller in light of the linearity theory for alluvial channel flow

Abstract

Due to a lack of sufficient theoretical relations, equations for bed load transport in alluvial channel flow have been developed using a variety of empirical assumptions. A linear relationship exhibited in the complex interactions among the three essential components of a river (channel geometry, bed load transport and flow resistance) has led this study to develop a more accurate form of the Meyer‐Peter and Müller (1948, hereafter MPM) relationship, one of the world's most widely used bed load transport equations. This study demonstrates that the application of linearity theory can significantly improve its performance. On the basis of the dataset originally used by MPM, it is shown that the applicable form of the Manning‐Strickler flow resistance relationship can be very satisfactorily determined. The MPM equation is consequently found to be expressible more accurately as Φ = 6[ητb* − 0.047]5/3, where Φ, η and τ*b are the normalized, dimensionless bed load transport rate, bed‐form correction, and flow‐strength parameters, respectively.