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A Ginzburg-Landau model for linear global modes in open shear flows

Gupta, V., He, W. ORCID: 0000-0002-2633-6114, Wan, M. , Chen, S. & Li, L. K. B. (2020). A Ginzburg-Landau model for linear global modes in open shear flows. Journal of Fluid Mechanics, 904, A31. doi: 10.1017/jfm.2020.691

Abstract

The Ginzburg–Landau equation (GLE) can phenomenologically model several key features of non-equilibrium systems including those in fluid mechanics. Its validity in real flows, however, remains questionable. Here, we show that the linear GLE can be formulated such that it has the same Wentzel–Kramers–Brillouin (WKB) approximation as for the linear global stability problem in open shear flows. We use the GLE to model the linear global modes of three different wakes and find that it can accurately capture the linear growth rate and frequency to first order in the WKB approximation. Furthermore, we find that it can also provide the shapes of the direct and adjoint eigenvectors and the regions of maximal structural sensitivity. The proposed model requires only the basic flow as input, but gives robust predictions and is computationally inexpensive. As well as opening up new possibilities for GLE-based control strategies, the proposed model makes accurate stability calculations possible, even for some computationally intractable open shear flows.

Publication Type: Article
Additional Information: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher Keywords: wakes
Subjects: T Technology > TJ Mechanical engineering and machinery
T Technology > TL Motor vehicles. Aeronautics. Astronautics
Departments: School of Science & Technology > Engineering
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