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- Title
Similarity Solutions for Unsteady Gravity-Driven Slender Rivulets.
- Authors
Yatim, Y. M.; Duffy, B. R.; Wilson, S. K.; Hunt, R.
- Abstract
The lubrication approximation is used to analyse unsteady gravity-driven flow of slender non-uniform rivulets on an inclined plane. Two distinct unsteady similarity solutions are obtained, corresponding to rivulets whose cross-sectional profiles are ‘single-humped’ and ‘double-humped’, respectively. Each solution represents both a sessile rivulet that narrows and thins with distance down the plane and a pendent rivulet that widens and thickens with distance down the plane. Moreover, the sessile rivulets widen and thicken with time and the pendent rivulets narrow and thin with time, the ‘nose’ of the rivulet being stationary in each case; in particular, the solutions for sessile rivulets exhibit a finite-time blow-up, becoming singular everywhere at some instant. The effect of small perturbations superposed on the similarity solutions is investigated numerically.
- Subjects
GRAVITY; INCLINED planes; PERTURBATION theory; MATHEMATICAL physics; NUMERICAL analysis
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2011, Vol 64, Issue 4, p455
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbr014