Asymptotic regimes of ridge and rift formation in a thin viscous sheet model

• Autores: Perazzo, C.A.; Gratton, J.
• Año de publicación: 2008
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Phys. Fluids 2008;20(4)
• Materia: Asymptotic regimes; Asymptotics; Dam-breaks; Dry region; Linear phase; Self-similar; Thin viscous sheet; Uniform layer; Multiphase flow; Asymptotic analysis; Newtonian liquids; Ocean currents; Viscosity; Separation; Dams; Ridge; Rift; Viscous dam; Viscous sheet model; Asymptotic analysis; Dams; Newtonian liquids; Ocean currents; Viscosity
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

We numerically and theoretically investigate the evolution of the ridges and rifts produced by the convergent and divergent motions of two substrates over which an initially uniform layer of a Newtonian liquid rests. We put particular emphasis on the various asymptotic self-similar and quasi-self-similar regimes that occur in these processes. During the growth of a ridge, two self-similar stages occur; the first takes place in the initial linear phase, and the second is obtained for a large time. Initially, the width and the height of the ridge increase as t 1/2. For a very large time, the width grows as t 3/4, while the height increases as t 1/4. On the other hand, in the process of formation of a rift, there are three self-similar asymptotics. The initial linear phase is similar to that for ridges. The second stage corresponds to the separation of the current in two parts, leaving a dry region in between. Last, for a very large t, each of the two parts in which the current has separated approaches the self-similar viscous dam break solution. © 2008 American Institute of Physics.
Fil:Perazzo, C.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Gratton, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.