ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
Flow of incompressible Newtonian liquid films is governed by the Navier–Stokes system with shear-free, balanced-normal-stress, and kinematic boundary conditions at the free surface. This system is solved here for the evolution of finite-amplitude two-dimensional disturbances to otherwise steady flow down a vertical plate by means of a finite element method adapted for free boundary problems. When flow is specified to be spatially periodic, fully developed steady flows that ensue approach time-periodic states, i.e., waves, the finite amplitude of which depends upon their wavelength. The family of time-periodic states connects to the steady, fully developed flow at a Hopf bifurcation that lies at a critical disturbance length, in agreement with the Orr–Sommerfeld analysis. Initial disturbances to flow down a plate of finite length grow as they propagate downward. In all cases studied here, however, steady flow is eventually approached.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.866286
