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Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane
Liu R(刘荣); Liu QS(刘秋生); Liu R
Source PublicationPhysics of Fluids
AbstractThe nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]
KeywordFluid-flow Stability Growth Layer
Indexed BySCI
WOS IDWOS:000281151200014
WOS Research AreaMechanics ; Physics
WOS SubjectMechanics ; Physics, Fluids & Plasmas
Funding OrganizationNational Foundation of China [10772185, 50890182] ; Chinese Academy of Sciences [KGCX-SW-409]
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Cited Times:13[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Corresponding AuthorLiu R
Recommended Citation
GB/T 7714
Liu R,Liu QS,Liu R. Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane[J]. Physics of Fluids,2010,22(7):74101.
APA 刘荣,刘秋生,&Liu R.(2010).Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane.Physics of Fluids,22(7),74101.
MLA 刘荣,et al."Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane".Physics of Fluids 22.7(2010):74101.
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