2 results
Bedforms in a turbulent stream: ripples, chevrons and antidunes
- Bruno Andreotti, Philippe Claudin, Olivier Devauchelle, Orencio Durán, Antoine Fourrière
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- Journal:
- Journal of Fluid Mechanics / Volume 690 / 10 January 2012
- Published online by Cambridge University Press:
- 28 November 2011, pp. 94-128
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The interaction between a turbulent flow and a granular bed via sediment transport produces various bedforms associated with distinct hydrodynamical regimes. In this paper, we compare ripples (downstream-propagating transverse bedforms), chevrons and bars (bedforms inclined with respect to the flow direction) and antidunes (upstream-propagating bedforms), focusing on the mechanisms involved in the early stages of their formation. Performing the linear stability analysis of a flat bed, we study the asymptotic behaviours of the dispersion relation with respect to the physical parameters of the problem. In the subcritical regime (Froude number smaller than unity), we show that the same instability produces ripples or chevrons depending on the influence of the free surface. The transition from transverse to inclined bedforms is controlled by the ratio of the saturation length , which encodes the stabilizing effect of sediment transport, to the flow depth , which determines the hydrodynamical regime. These results suggest that alternate bars form in rivers during flooding events, when suspended load dominates over bedload. In the supercritical regime , the transition from ripples to antidunes is also controlled by the ratio . Antidunes appear around resonant conditions for free surface waves, a situation for which the sediment transport saturation becomes destabilizing. This resonance turns out to be fundamentally different from the inviscid prediction. Their wavelength selected by linear instability mostly scales on the flow depth , which is in agreement with existing experimental data. Our results also predict the emergence, at large Froude numbers, of ‘antichevrons’ or ‘antibars’, i.e. bedforms inclined with respect to the flow and propagating upstream.
Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening
- ANTOINE FOURRIÈRE, PHILIPPE CLAUDIN, BRUNO ANDREOTTI
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- Journal:
- Journal of Fluid Mechanics / Volume 649 / 25 April 2010
- Published online by Cambridge University Press:
- 13 April 2010, pp. 287-328
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It is widely accepted that both ripples and dunes form in rivers by primary linear instability; the wavelength of the former scaling on the grain size and that of the latter being controlled by the water depth. We revisit here this problem in a theoretical framework that allows to give a clear picture of the instability in terms of dynamical mechanisms. A multi-scale description of the problem is proposed, in which the details of the different mechanisms controlling sediment transport are encoded into three quantities: the saturated flux, the saturation length and the threshold shear stress. Hydrodynamics is linearized with respect to the bedform aspect ratio. We show that the phase shift of the basal shear stress with respect to the topography, responsible for the formation of bedforms, appears in an inner boundary layer where shear stress and pressure gradients balance. This phase shift is sensitive to the presence of the free surface, and the related effects can be interpreted in terms of standing gravity waves excited by topography. The basal shear stress is dominated by this finite depth effect in two ranges of wavelength: when the wavelength is large compared to the flow depth, so that the inner layer extends throughout the flow, and in the resonant conditions, when the downstream material velocity balances the upstream wave propagation. Performing the linear stability analysis of a flat sand bed, the relation between the wavelength at which ripples form and the flux saturation length is quantitatively derived. It explains the discrepancy between measured initial wavelengths and predictions that do not take this lag between flow velocity and sediment transport into account. Experimental data are used to determine the saturation length as a function of grain size and shear velocity. Taking the free surface into account, we show that the excitation of standing waves has a stabilizing effect, independent of the details of the flow and sediment transport models. Consequently, the shape of the dispersion relation obtained from the linear stability analysis of a flat sand bed is such that dunes cannot result from a primary linear instability. We present the results of field experiments performed in the natural sandy Leyre river, which show the formation of ripples by a linear instability and the formation of dunes by a nonlinear pattern coarsening limited by the free surface. Finally, we show that mega-dunes form when the sand bed presents heterogeneities such as a wide distribution of grain sizes.