The stability and flow of a rivulet driven by interfacial shear and gravity

In this paper, the steady unidirectional flow of a rivulet, driven by interfacial shear and gravity, is considered. When the aspect ratio of the rivulet is small the pressure, velocity, flux and cross-sectional shape are determined in the form of asymptotic power series. The problem is also solved numerically without the small aspect ratio assumption. The analytical and numerical results are compared to test the range of validity of the asymptotics. Both sets of results are also compared with existing experimental data. Finally, the rivulet energy is considered to determine whether it is energetically favourable for a rivulet to split. (C) 2003 Elsevier Ltd. All rights reserved.