INVESTIGADORES
MARINO Beatriz Maria
artículos
Título:
Noncircular converging flows in viscous gravity currents
Autor/es:
DIEZ, JA; THOMAS, LP; BETELU, S; GRATTON, R; MARINO, BM; GRATTON, J; ARONSON, DG; ANGENENT, SB
Revista:
PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS
Editorial:
Americal Physical Society
Referencias:
Año: 1998 vol. 58 p. 6182 - 6187
ISSN:
1063-651X
Resumen:
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 cavitys 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 k>~2. These nonlinear stability calculations show that the circle is unstable in the presence of the mode k=2
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.