Instability of tilted shear flow in a strongly stratified and viscous medium
File(s)
Accepted version
Author(s)
Fung, Lloyd
Hwang, Yongyun
Type
Journal Article
Abstract
It is well known that stratification can stabilise shear flow. In a vertical shear flow, the Miles-Howard’s criterion firmly indicates that flow should be stable if the local Richardson number is greater than one fourth. However, if shear is tilted with a non-zero angle from vertical, an instability can arise even under very strong stratification, and such an instability was recently observed in a titled wake flow at low Reynolds number (Meunier 2012, J. Fluid Mech., 699:174). In the present study, we showed that in the limit of low Froude number and low Reynolds number, the linearised equations of motion could be reduced to the Orr-Sommerfeld equation on the horizontal plane, except the viscous term that contains vertical dissipation. Based on this equation, it is demonstrated that the low-Froude-number mode would be a horizontal inflectional instability, and should remain two dimensional at small tilting angles. It is further shown that the emergence of small vertical velocity at finite Froude number modifies the horizontal inflectional instability and leads to paradoxically stabilising buoyancy force on increasing Froude number. Finally, an absolute instability analysis is performed, revealing qualitatively good agreement with the experimental result.
Date Issued
2021-07-31
Date Acceptance
2020-01-06
Citation
IUTAM Bookseries, 2021, 38, pp.379-389
ISSN
1875-3507
Publisher
Springer Verlag
Start Page
379
End Page
389
Journal / Book Title
IUTAM Bookseries
Volume
38
Copyright Statement
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022. The final publication is available at Springer via https://link.springer.com/chapter/10.1007%2F978-3-030-67902-6_33
Identifier
http://arxiv.org/abs/1909.11376v1
Subjects
physics.flu-dyn
physics.flu-dyn
Publication Status
Published
Date Publish Online
2021-07-31