Practical sand transport formula for non-breaking waves and currents

Dominic A. van der A, Jan S. Ribberink, Jebbe J. van der Werf, Thomas O'Donoghue, René H. Buijsrogge, Wouter M. Kranenburg

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Many existing practical sand transport formulae for the coastal marine environment are restricted to a limited range of hydrodynamic and sand conditions. This paper presents a new practical formula for net sand transport induced by non-breaking waves and currents. The formula is especially developed for cross-shore sand transport under wave-dominated conditions and is based on the semi-unsteady, half wave-cycle concept, with bed shear stress as the main forcing parameter. Unsteady phase-lag effects between velocities and concentrations, which are especially important for rippled bed and fine sand sheet-flow conditions, are accounted for through parameterisations. Recently-recognised effects on the net transport rate related to flow acceleration skewness and progressive surface waves are also included. To account for the latter, the formula includes the effects of boundary layer streaming and advection effects which occur under real waves, but not in oscillatory tunnel flows. The formula is developed using a database of 226 net transport rate measurements from large-scale oscillatory flow tunnels and a large wave flume, covering a wide range of full-scale flow conditions and uniform and graded sands with median diameter ranging from 0.13 mm to 0.54 mm. Good overall agreement is obtained between observed and predicted net transport rates with 78% of the predictions falling within a factor 2 of the measurements. For several distinctly different conditions, the behaviour of the net transport with increasing flow strength agrees well with observations, indicating that the most important transport processes in both the rippled bed and sheet flow regime are well captured by the formula. However, for some flow conditions good quantitative agreement could only be obtained by introducing separate calibration parameters. The new formula has been validated against independent net transport rate data for oscillatory flow conditions and steady flow conditions.
Original languageEnglish
Pages (from-to)26-42
Number of pages17
JournalCoastal Engineering
Issue number-
Early online date28 Jan 2013
Publication statusPublished - Jun 2013

Bibliographical note

Open Access funded by Engineering and Physical Sciences Research Council
Under a Creative Commons license

This work is part of the SANTOSS project (‘SANd Transport in OScillatory flows in the Sheet-flow regime’) funded by the UK's EPSRC (GR/T28089/01) and STW in The Netherlands (TCB.6586). JW acknowledges Deltares strategic research funding under project number 1202359.09. Richard Soulsby is gratefully acknowledged for valuable discussions and feedback on the formula during the SANTOSS project.


  • sediment transport formula
  • sheet flow
  • ripples
  • bed shear stress
  • phase lag effects
  • advection effects


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