Details
| Original language | English |
|---|---|
| Pages (from-to) | 271-293 |
| Number of pages | 23 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Volume | 13 |
| Issue number | 2 |
| Publication status | Published - 4 Feb 2010 |
Abstract
We study the radial movement of an incompressible fluid located in a Hele-Shaw cell rotating at a constant angular velocity in the horizontal plane. Within an analytic framework, local existence and uniqueness of solutions is proved, and it is shown that the unique rotationally invariant equilibrium of the flow is unstable. There are, however, other time-independent solutions: using surface tension as a bifurcation parameter we establish the existence of global bifurcation branches consisting of stationary fingering patterns. The same results can be obtained by fixing the surface tension while varying the angular velocity. Finally, it is shown that the equilibria on a global bifurcation branch converge to a circle as the surface tension tends to infinity, provided they stay suitably bounded.
Keywords
- Bifurcation, Equilibria, Fingering patterns, Hele-Shaw cell, Well-posedness
ASJC Scopus subject areas
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Mathematical Fluid Mechanics, Vol. 13, No. 2, 04.02.2010, p. 271-293.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Well-Posedness, Instabilities, and Bifurcation Results for the Flow in a rotating Hele-Shaw cell
AU - Ehrnström, Mats
AU - Escher, Joachim
AU - Matioc, Bogdan-Vasile
PY - 2010/2/4
Y1 - 2010/2/4
N2 - We study the radial movement of an incompressible fluid located in a Hele-Shaw cell rotating at a constant angular velocity in the horizontal plane. Within an analytic framework, local existence and uniqueness of solutions is proved, and it is shown that the unique rotationally invariant equilibrium of the flow is unstable. There are, however, other time-independent solutions: using surface tension as a bifurcation parameter we establish the existence of global bifurcation branches consisting of stationary fingering patterns. The same results can be obtained by fixing the surface tension while varying the angular velocity. Finally, it is shown that the equilibria on a global bifurcation branch converge to a circle as the surface tension tends to infinity, provided they stay suitably bounded.
AB - We study the radial movement of an incompressible fluid located in a Hele-Shaw cell rotating at a constant angular velocity in the horizontal plane. Within an analytic framework, local existence and uniqueness of solutions is proved, and it is shown that the unique rotationally invariant equilibrium of the flow is unstable. There are, however, other time-independent solutions: using surface tension as a bifurcation parameter we establish the existence of global bifurcation branches consisting of stationary fingering patterns. The same results can be obtained by fixing the surface tension while varying the angular velocity. Finally, it is shown that the equilibria on a global bifurcation branch converge to a circle as the surface tension tends to infinity, provided they stay suitably bounded.
KW - Bifurcation
KW - Equilibria
KW - Fingering patterns
KW - Hele-Shaw cell
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=79958803775&partnerID=8YFLogxK
U2 - 10.1007/s00021-010-0022-1
DO - 10.1007/s00021-010-0022-1
M3 - Article
AN - SCOPUS:79958803775
VL - 13
SP - 271
EP - 293
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 2
ER -