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On the Rayleigh-Taylor instability for two uniform viscous incompressible flows

Content Provider	Springer Nature Link
Author	Jiang, Fei Jiang, Song Wang, Weiwei
Copyright Year	2014
Abstract	The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in (unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth (when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem. Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.
Starting Page	907
Ending Page	940
Page Count	34
File Format	PDF
ISSN	02529599
Journal	Chinese Annals of Mathematics, Series B
Volume Number	35
Issue Number	6
e-ISSN	18606261
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-10-24
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Rayleigh-Taylor instability Viscous incompressible flows Global instability Interfacial stability and instability Navier-Stokes equations Mathematics Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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