On Bagnold's sediment transport equation in tidal marine environments and the practical definition of bedload



    1. Comparative Sedimentology Division, Institute of Earth Sciences, University of Utrecht, The Netherlands
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      Permanent address: Ministry of Geology and Mineral Resources, Marine Geological Survey, 526 Yan An Road West, Shanghai, China.


Bagnold's sediment transport equation has proved to be important in studying tidal marine environments. This paper discusses three problems concerning Bagnold's transport equation and its practical application:

  • 1Bagnold's suspended-load transport equation inline image and the total-load transport equation inline image with inline image are incorrect from the viewpoint of energy conservation. In these equations the energy loss due to bedload transport has been counted twice. The correct form should be inline image for suspended-load transport and inline image for total-load transport with inline image
  • 2The commonly used Bagnold's transport coefficient K varies as a non-linear function of the dimensionless excess shear stress, which can be represented best by the power law inline image, where the coefficient A and exponent B depend on sediment grain size D. The empirical values of A and B for fine to medium grained sands are determined using Guy et al.'s (1966) flume-experiment data.
  • 3The sediment transport rates predicted from this equation are compared with bedform migration measurements in the flume and the field. This comparison shows that the sediment transport rates measured from bedform migrations are higher than the predicted bedload transport rates, but comparable to the calculated total-load (bedload plus intermittent suspended-load) transport rates. This indicates that bedform migration involves both bedload and intermittent suspended-load transport. As a logical conclusion, bedform migration data should be compared with Bagnold's total-load transport equation rather than with his bedload transport equation. In this respect the term ‘bed material’ might be more appropriate than the term ‘bedload’ for estimating sediment transport rate from bedform migration data.

The sediment transport rates predicted from this modified Bagnold transport equation are in good agreement with field measurements of bedform migration rates in four individual tidal marine environments, which cover a wide range of sediment grain size, flow velocity and bedform conditions (ranging from small ripples, megaripples to sandwaves).