Geodesic
An axisymmetric model of the ring pattern formation in free-surface two-layered creeping flow
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2009), pp. 63-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The axisymmetric model based on simplified equations of incompressible viscous fluid is developed to investigate the evolution of free-surface two-layered creeping flow subjected by the uplift of the substrate's block. We numerically solve the nonlinear governing equations and perform the small-amplitude analysis of the behavior of both fluid interfaces. The main result is that a ring pattern does occur on the upper surface provided that the density of the lower layer is greater then that of the upper one. The presented model may be of interest for geophysics to study large-scale ring structures on the Earth and other solid planets.
Keywords: Stokes flow, multi-layered flows, long-wave approximation, nonlinear diffusion, ring structures. 
@article{VUU_2009_2_a6,
     author = {V. V. Pack},
     title = {An axisymmetric model of the ring pattern formation in free-surface two-layered creeping flow},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {63--74},
     year = {2009},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2009_2_a6/}
}
TY  - JOUR
AU  - V. V. Pack
TI  - An axisymmetric model of the ring pattern formation in free-surface two-layered creeping flow
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2009
SP  - 63
EP  - 74
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VUU_2009_2_a6/
LA  - ru
ID  - VUU_2009_2_a6
ER  - 
%0 Journal Article
%A V. V. Pack
%T An axisymmetric model of the ring pattern formation in free-surface two-layered creeping flow
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2009
%P 63-74
%N 2
%U http://geodesic.mathdoc.fr/item/VUU_2009_2_a6/
%G ru
%F VUU_2009_2_a6
V. V. Pack. An axisymmetric model of the ring pattern formation in free-surface two-layered creeping flow. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2009), pp. 63-74. http://geodesic.mathdoc.fr/item/VUU_2009_2_a6/

[1] Mikhailov V. O., “Matematicheskaya model protsessa evolyutsii struktur, obrazuyuschikhsya v rezultate vertikalnykh dvizhenii”, Izv. AN SSSR. Fizika Zemli, 1983, no. 6, 3–18

[2] Hu J., Millet S., Botton V., Ben Hadid H., and Henry D., “Inertialess temporal and spatio-temporal stability analysis of the two-layer film flow with density stratification”, Phys. of Fluids, 18 (2006), 104101 | DOI | MR | Zbl

[3] Loewenherz D. S. and Lawrence C. J., “The effect of viscosity stratification on the instability of a free surface flow at low Reynolds number”, Phys. of Fluids A, 1:10 (1989), 1686–1693 | DOI | Zbl

[4] Sedov L. I., Mekhanika sploshnoi sredy, v. 2, Nauka, M., 1970, 492 pp. | MR

[5] Pak V. V., Kuptsov K. G., Ovchinnikov M. O., “Chislennoe modelirovanie evolyutsii gorizontalno-sloistykh morfostruktur osadochnykh basseinov”, Informatika i modelirovanie v okeanologicheskikh issledovaniyakh, Dalnauka, Vladivostok, 1999, 225–233

[6] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977, 735 pp. | MR

[7] Arsenin V. A., Metody matematicheskoi fiziki i spetsialnye funktsii, Nauka, M., 1974, 432 pp. | MR

[8] Stazhevskii S. B., “O vklade koltsevykh struktur v napryazhenno-deformirovannoe sostoyanie okrain tikhookeanskogo tipa i prirode tsunami”, Fizicheskaya mezomekhanika, 10:1 (2007), 59–72 | MR

[9] Ebbing J., Janle P., Koulouris J., Milkereit B., “3D gravity modelling of the Chicxulub impact structure”, Planetary and Space Science, 49 (2001), 599–609 | DOI

[10] Terkot D., Shubert Dzh., Geodinamika. Geologicheskoe prilozhenie fiziki sploshnykh sred, v. 2, Mir, M., 1985, 360 pp.

[11] Snoeijer J. H., “Free-surface flows with large slopes: Beyond lubrication theory”, Phys. of Fluids, 18 (2006), 021701 | DOI