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Small is beautiful: Upscaling from microscale laminar to natural turbulent rivers

Abstract : [1] The use of microscale experimental rivers (with flow depths of the order of a few millimeters) to investigate natural processes such as alluvial fans dynamics, knickpoints migration, and channel morphologies, such as meandering and braiding has become increasingly popular in recent years. This raises the need to address the issue of how to extrapolate results from the experimental microscale at which flow is laminar to the scale of natural turbulent rivers. We address this question by performing measurements of average flow velocity and sediment transport in an experimental laminar river. The average flow velocity is correctly predicted from the Navier-Stokes equation solved for a steady uniform laminar flow. Laminar sediment transport is found to be consistent with the law of Meyer-Peter and Müller (1948) commonly used to describe sediment transport in natural turbulent rivers. We also show that surface tension is important only if the microscale river width is on the order of or smaller than the capillary length. These results allow us to demonstrate that the evolution of longitudinal bed profiles of turbulent and laminar rivers are governed by identical dimensionless equations and therefore follow the same dynamics. Differences of time and length scales at work in experimental and natural rivers are mainly encoded in the expression of two parameters, a diffusion coefficient and a threshold slope. On the basis of this analysis, we derive a set of equations allowing us to rescale bed elevation, downstream distance, time, and uplift rate from an experimental microscale river to the field scale. Finally, we show how this set of equations can be used to rescale these same parameters in the case of a temporally varying discharge. Citation: Malverti, L., E. Lajeunesse, and F. Métivier (2008), Small is beautiful: Upscaling from microscale laminar to natural turbulent rivers,
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L Malverti, E Lajeunesse, F D Métivier. Small is beautiful: Upscaling from microscale laminar to natural turbulent rivers. Journal of Geophysical Research, 2008, 331, pp.105 - 105. ⟨10.1029/2007JF000974⟩. ⟨hal-01499448⟩



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