Linear stability and energy growth of viscosity stratified flows

Hooper, Alison P.; Malik, Satish V.

Abstract

The non-normality of the Orr-Sommerfeld equation leads to the possibility of disturbance growth even though all eigenvalues are stable. In single-fluid flow the disturbance growth converges to a limit once the number of modes exceeds a minimum number. In the case of a two-fluid flow, however, convergence is not found. The problem of nonconvergence is due to the presence of the interface and the corresponding interfacial mode. The interface is replaced with a miscible layer of variable viscosity. When the thickness of the miscible layer is approximately equal to the thickness of the critical layer, the flow resembles two-fluid flow and one of the modes starts behaving like the interfacial mode. © 2005 American Institute of Physics.

Citation

Hooper, A. P., & Malik, S. V. (2005). Linear stability and energy growth of viscosity stratified flows. Physics of Fluids, 17(2), 1-8. https://doi.org/10.1063/1.1834931

• Journal Article Type: Article
• Publication Date: Jan 1, 2005
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Publisher: AIP Publishing
• Peer Reviewed: Not Peer Reviewed
• Volume: 17
• Issue: 2
• Pages: 1-8
• DOI: https://doi.org/10.1063/1.1834931
• Keywords: linear stability, energy growth, viscosity stratified flow
• Public URL: https://uwe-repository.worktribe.com/output/1052047
• Publisher URL: http://dx.doi.org/10.1063/1.1834931