Three-dimensional disturbances in channel flows

Hooper, Alison P.; Malik, Satish V.

Abstract

In this paper we conduct a linear stability analysis of three-dimensional two-fluid flows and use an energy method to comment on its stability. The governing equations are solved using a Chebyshev-tau D2 method that reduces the order of the coupled governing Orr-Sommerfeld and Squire equation and hence achieves more accurate results. A new norm, called the M-norm, is defined to overcome the problem of nonconvergence of the disturbance energy. The maximum amplification of O(103) is achieved for streamwise independent disturbances due to the "lift-up effect," as is the case of three-dimensional single-fluid flow. In contrast to two-dimensional flows, where the adjoint of the leading mode influences the growth, the three-dimensional single-fluid flow growth is influenced by the adjoint of the second mode. Although most growth in three-dimensional two-fluid flow is due to the contribution of the adjoint of the second mode, at large time the interfacial mode contributes to most growth. © 2007 American Institute of Physics.

• Journal Article Type: Article
• Publication Date: Jan 1, 2007
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: AIP Publishing
• Peer Reviewed: Not Peer Reviewed
• Volume: 19
• Issue: 5
• Pages: 0521021- 05210218
• DOI: https://doi.org/10.1063/1.2721600
• Keywords: three-dimensional disturbances, channel flows
• Public URL: https://uwe-repository.worktribe.com/output/1027808
• Publisher URL: http://dx.doi.org/10.1063/1.2721600