title: Linear stability analysis in a liquid layer with a surface velocity gradient.
abstract: A case of combined planar Couette-Poiseuille flow corresponding to vanishing horizontal flux has been generalized by the introduction of a model for the surface velocity gradient. A relation corresponding to the Orr-Sommerfeld equation has been derived for this model. The critical value of the surface velocity gradient has been obtained. At the critical point, the corresponding critical Reynolds number equals infinity. Using an approximated method we estimated the behavior of the critical Reynolds number for a slightly overcritical surface velocity gradient.
authors.affiliation: Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland. bialecki@if.pw.edu.pl
authors.forename: Jarosław
authors.initials: J
authors.lastname: Białecki
authors.forename: Janusz A
authors.initials: JA
authors.lastname: Hołyst