Journal of Fluid Mechanics

Papers

The dam-break problem for viscous fluids in the high-capillary-number limit

C. ANCEYa1 c1, S. COCHARDa2 and N. ANDREINIa1

a1 School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

a2 Department of Mathematics, University of British Columbia, Vancouver V6K 2A5, Canada

Abstract

Experiments were undertaken to investigate dam-break flows where a finite volume of highly viscous fluid (glucose with viscosity μ ≈ 350 Pa s) maintained behind a lock gate was released into a horizontal or inclined flume. The resulting sequence of flow-depth profiles was tracked using a three-dimensional visualization system. In the low-Reynolds-number and high-capillary-number limits, analytical solutions can be obtained from the Navier–Stokes equations using lubrication theory and matched asymptotic expansions. At shallow slopes, similarity solutions can also be worked out. While the variation in the front position scaled with time as predicted by theory for both horizontal and sloping flumes, there was a systematic delay in the front position observed. Moreover, taking a closer look at the experimental flow-depth profiles shows that they were similar, but they noticeably deviated from the theoretical similarity form for horizontal planes. For sloping beds, the flow-depth profile is correctly predicted provided that different scalings are used at shallow and large slopes.

(Received March 21 2008)

(Revised November 18 2008)

Correspondence:

c1 Email address for correspondence: christophe.ancey@epfl.ch

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