Wave formation in laminar flow down an inclined plane

摘要: This paper deals theoretically with a problem of hydrodynamic stability characterized by small values the Reynolds number R . The primary flow whose is examined consists uniform laminar stream viscous liquid running down an inclined plane under action gravity, being bounded on one side free surface influenced tension. thus has direct bearing properties thin films such as have important uses in chemical engineering. Numerous experiments past shown that wall noticeably agitated waves except when quite small; vertical water film, for instance, may be observed until reduced to some value rather less than 10. present treatment accordingly based methods approximation suited fairly low , and thereby avoids severe mathematical difficulties usual problems at high formulation resembles given Yih (1954); but method solution differs from his, respective results are conflict. In particular, there dis-agreement over matter strictly very contrast previous conclusions, it here always unstable: is, class undamped exists all finite However, rates amplification unstable become made small, their wavelengths large; this provides satisfactory explanation apparent absence experimental observations, also wide scatter among existing estimates ‘quasi-critical’ below which undetectable. view controversial nature these results, emphasis various points agreement between work established theory roll waves; latter gives clear picture physical mechanism wave formation gravitational flows, its light obtained appear entirely reasonable. conditions governing neutral worked out third order parameter accurate then justified adequate basis easily workable providing ready check experiment, used predict observable should first develop length velocity waves. These three predictions compared found Binnie (1957), substantially confirmed.