Unsteady Rivulet Flow
M. Yatim (Department of Mathematics, University of Strathclyde, Glasgow), S. K. Wilson, B. R. Duffy and R. Hunt (Department of Mathematics, University of Strathclyde, Glasgow)
Rivulets occur commonly in a wide range of geophysical, biological and industrial contexts. In the present study the lubrication approximation is used to analyse the unsteady gravity-driven flow of slender non-uniform rivulets on an inclined plane. Adopting an analogous approach to that of Smith (J. Fluid Mech. 58, 1973, 275-288) and Duffy & Moffatt (Euro. J. Appl. Math. 8, 1997, 37-47) in their analyses of steady rivulet flow, we obtain an unsteady similarity solution which predicts that the rivulet widens or narrows according to the negative one quarter power of time and thickens or thins like the negative one half power of time. Cross-sectional profiles can be either ``single-humped'' or ``double-humped''.