We study the filling of a dry region (cavity) within a viscous liquid layer on a horizontal plane. In our experiments the cavities are created by removable dams of various shapes surrounded by a silicon oil, and we measure the evolution of the cavity’s boundaries after removal of the dams. Experimental runs with circular, equilateral triangular, and square dams result in circular collapse of the cavities. However, dams whose shapes lack these discrete rotational symmetries, for example, ellipses, rectangles, or isosceles triangles, do not lead to circular collapses. Instead, we find that near collapse the cavities have elongated oval shapes. The axes of these ovals shrink according to different power laws, so that while the cavity collapses to a point, the aspect ratio is increasing. The experimental setup is modeled within the lubrication approximation. As long as capillarity is negligible, the evolution of the fluid height is governed by a nonlinear diffusion equation. Numerical simulations of the experiments in this approximation show good agreement up to the time where the cavity is so small that surface tension can no longer be ignored. Nevertheless, the noncircular shape of the collapsing cavity cannot be due to surface tension which would tend to round the contours. These results are supplemented by numerical simulations of the evolution of contours which are initially circles distorted by small sinusoidal perturbations with wave numbers [Formula Presented] These nonlinear stability calculations show that the circle is unstable in the presence of the mode [Formula Presented] and stable in its absence. The same conclusion is obtained from the linearized stability analysis of the front for the known self-similar solution for a circular cavity. © 1998 The American Physical Society.
Documento: | Artículo |
Título: | Noncircular converging flows in viscous gravity currents |
Autor: | Diez, J.A.; Thomas, L.P.; Betelú, S.; Gratton, R.; Marino, B.; Gratton, J.; Aronson, D.G.; Angenent, S.B. |
Filiación: | Instituto de Física Arroyo Seco, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, Tandil, 7000, Argentina Instituto Nacional de Física de Plasmas Consejo Nacional de Investigaciones Cientificas y Tecnicas, Laboratorio de Fisica de Plasma Departamento de Física, Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires, Pabellón I Ciudad Universitaria, Buenos Aires, 1428, Argentina School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, United States Department of Mathematics, University of Wisconsin, Madison, WI, 53706, United States |
Año: | 1998 |
Volumen: | 58 |
Número: | 5 |
Página de inicio: | 6182 |
Página de fin: | 6187 |
DOI: | http://dx.doi.org/10.1103/PhysRevE.58.6182 |
Título revista: | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
Título revista abreviado: | Phys Rev E. |
ISSN: | 1063651X |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1063651X_v58_n5_p6182_Diez |