A theory to explain and predict the onset of bed erosion under turbulent flow


In hydraulics, Shields parameter represents a non-dimensional number used to predict the initiation of motion of sediment in an open channel (i.e. bed erosion). This now-classical approach was first proposed by A. Shields in the 1930’s and is based on the time–space-averaged bed shear stress. However, past reviews of Shields-based incipient motion studies have revealed the impossibility of defining an accurate and universal threshold of motion based on the time–space-averaged shear stress. Recently, experimental studies have promoted an alternative approach to predict the incipient motion threshold, which is based on the impulse of the flow-induced force exerted on the bed particles. These experimental studies have been accompanied by theoretical analyses relating forces and their durations, but containing certain constraints and caveats that could potentially be improved upon.

Generally, an in-depth cross examination of recent literature reveals that most of the proposed theoretical approaches underpinning the impulse-based criterion depend critically on empirical coefficients such as drag, lift and energy transfer. To address this, University of Southampton scientists Dr. Sergio Maldonado and Dr. Gustavo de Almeida recently proposed to employ the work–energy principle to derive a prediction of the fundamental impulse threshold that the destabilizing hydrodynamic force must overcome in order to achieve full particle dislodgement. Their aim was to provide a simple, yet rigorous, theoretical analysis for such an impulse-based criterion. Their work has been published in the Journal of Fluid Mechanics.

Their proposed criterion is defined in terms of the time-dependent force exerted on a particle by the flow (instead of the flow variables producing said force), which enabled the two scholars to derive a relation that is simple and independent of empirical coefficients such as drag and lift. The resulting criterion, which only depends on the mobile particle’s size and mass for a given bed setting, was investigated.

The authors reported that the derived impulse-based criterion for dislodgement showed excellent agreement with previously published experimental data. Specifically, their work yielded a virtually exact prediction of the critical impulse and predicted well the fundamental threshold for particle dislodgement even when using the pseudo-impulse reported in a previous publication.

In summary, based on purely theoretical considerations, Maldonado & de Almeida unveiled a new criterion for the critical impulse that the destabilizing hydrodynamic force must exceed to achieve particle dislodgement. They proposed an expression which they derived from the work–energy principle and validated for the bed setting depicted, with outstanding results. In a statement to Advances in Engineering, Dr. Sergio Maldonado commented that they were auspicious their work could be used as a much needed theoretical framework to guide the design of future experiments aimed to study hydrodynamic impulse as a criterion for particle dislodgement, and thus improve significantly our understanding of sediment transport in fluvial and coastal environments.

predict the onset of bed erosion under turbulent flow - Advances in Engineering

About the author

Dr Sergio Maldonado is a lecturer (Assistant Professor) at the Faculty of Engineering and Physical Sciences, University of Southampton, UK. He obtained his PhD in Environmental Fluid Mechanics from the University of Edinburgh in 2015, and held a postdoctoral position at Stanford University prior to joining Southampton. His main research interest relate to the fundamental mechanics of water-sediment interaction and coastal engineering.


About the author

Dr Gustavo A. M. de Almeida is a lecturer (Assistant Professor) at the University of Southampton. He received a PhD in Hydraulic Engineering from UPC-BarcelonaTech in 2007 and prior to joining Southampton worked at the University of Newcastle Australia and University of Bristol as a postdoctoral research fellow. His main research interests are in the fields of fluvial hydrodynamics, sediment transport and river engineering.



S. Maldonado, G. de Almeida. Theoretical impulse threshold for particle dislodgement. Journal of Fluid Mechanics (2019), volume 863, page 893–903.

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