Turbulent and inertial roll waves in inclined film flow
- 1 May 1987
- journal article
- research article
- Published by AIP Publishing in Physics of Fluids
- Vol. 30 (5), 1259-1268
- https://doi.org/10.1063/1.866292
Abstract
Conditions for the onset of high Reynolds number roll waves on inclined interfaces are sought. The model equations of Dressler [Commun. Pure Appl. Math. 2, 149 (1949)] and Needham and Merkin [Proc. R. Soc. London Ser. A 3 9 4, 259 (1984)] are analyzed using dynamic singularity theory (normal form techniques) and numerical methods. A new family of roll‐wave solutions is discovered. They provide bounds and averages of the velocities of all roll waves at a given Froude number. These are favorably compared to the data of Brock [Proc. Am. Soc. Civ. Eng. 1 2, 2565 (1970)] and Brauner and Maron [Int. J. Heat Mass Transfer 2 5, 99 (1982)]. The average wave velocity is demonstrated to be approximately 1.5 times the average fluid velocity.Keywords
This publication has 19 references indexed in Scilit:
- On infinite period bifurcations with an application to roll wavesActa Mechanica, 1986
- An infinite period bifurcation arising in roll waves down an open inclined channelProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1986
- Wave formation on a vertical falling liquid filmAIChE Journal, 1985
- On roll waves down an open inclined channelProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- Simulation of the vertical flow of a thin, wavy film using a finite-element methodInternational Journal of Heat and Mass Transfer, 1984
- Characteristics of inclined thin films, waviness and the associated mass transferInternational Journal of Heat and Mass Transfer, 1982
- Classification and unfoldings of degenerate Hopf bifurcationsJournal of Differential Equations, 1981
- Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvaluesFunctional Analysis and Its Applications, 1975
- Finite amplitude side-band stability of a viscous filmJournal of Fluid Mechanics, 1974
- Mathematical solution of the problem of roll‐waves in inclined opel channelsCommunications on Pure and Applied Mathematics, 1949