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Critical slope for laminar transcritical shallow-water flows

Thual, Olivier and Lacaze, Laurent and Mouzouri, Miloud and Boutkhamouine, Brahim Critical slope for laminar transcritical shallow-water flows. (2015) Journal of Fluid Mechanics, 783. 1-11. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/jfm.2015.559

Abstract

Backwater curves denote the depth profiles of steady flows in a shallow open channel. The classification of these curves for turbulent regimes is commonly used in hydraulics. When the bottom slope I is increased, they can describe the transition from fluvial to torrential regimes. In the case of an infinitely wide channel, we show that laminar flows have the same critical height hc as that in the turbulent case. This feature is due to the existence of surface slope singularities associated to plug-like velocity profiles with vanishing boundary-layer thickness. We also provide the expression of the critical surface slope as a function of the bottom curvature at the critical location. These results validate a similarity model to approximate the asymptotic Navier–Stokes equations for small slopes I with Reynolds number Re such that ReI is of order 1.

Item Type:Article
Additional Information:Thanks to Cambridge University Press (CUP) editor. The original PDF of the article can be found at Journal of Fluid Mechanics website : http://journals.cambridge.org/action/displayJournal?jid=FLM#.VinfM6cy9pg
HAL Id:hal-01220472
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Laboratory name:
Funders:
RTRA STAE
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Deposited On:26 Oct 2015 12:57

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