Nonlinear instability of Hele-Shaw flows with smooth viscous profiles

abstract

• We rigorously derive nonlinear instability of Hele-Shaw flows moving with a constant velocity in the presence of smooth viscosity profiles where the viscosity upstream is lower than the viscosity downstream. This is a single-layer problem without any material interface. The instability of the basic flow is driven by a viscosity gradient as opposed to conventional interfacial Saffman-Taylor instability where the instability is driven by a viscosity jump across the interface. Existing analytical techniques are used in this paper to establish nonlinear instability. 2008 Elsevier Inc. All rights reserved.

authors

• Daripa, Prabir

published proceedings

• JOURNAL OF DIFFERENTIAL EQUATIONS

author list (cited authors)

• Daripa, P., & Hwang, H. J.

citation count

• 3

complete list of authors

• Daripa, Prabir||Hwang, Hyung Ju

publication date

• October 2008

publisher

• Elsevier  Publisher

published in

• Journal of Differential Equations  Journal

keywords

• Hele-shaw Flows
• Nonlinear Stability
• Spectral Theory
• Viscosity Gradient Driven Instability

Digital Object Identifier (DOI)

• 10.1016/j.jde.2008.07.012

start page

• 1819

end page

• 1837

volume

• 245

issue

• 7

URL

• http://dx.doi.org/10.1016/j.jde.2008.07.012