Healey, J (2019) Fractal sets of neutral curves for stably-stratified plane Couette flow. Journal of Fluid Mechanics. (In Press)

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Abstract

The linear stability of plane Couette flow is investigated when the plates are horizontal, and the fluid is stably stratified with a cubic basic density profile. The disturbances are treated as inviscid and diffusion of the density field is neglected. Previous studies have shown that this density profile can develop multiple neutral curves, despite the stable stratification, and the fact that plane Couette flow of homogeneous fluid is stable. It is shown that when the neutral curves are plotted with wave-angle on one axis, and location of the density in flexion point on the other axis, they produce a self-similar fractal pattern. The repetition on smaller and smaller scales occurs in the limit when the waves are highly oblique, i.e. longitudinal vortices almost aligned with the flow; the corresponding limit for two-dimensional waves is that of strong buoyancy/weak flow. The fractal set of neutral curves also represents a fractal of bifurcation points at which nonlinear solutions can be continued from the trivial state, and these may be helpful for understanding turbulent states. This may be the first example of a fractal generated by a linear ordinary differential equation.

Item Type: Article
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) will be available online via Cambridge University Press at https://www.cambridge.org/core/journals/journal-of-fluid-mechanics - please refer to any applicable terms of use of the publisher.
Uncontrolled Keywords: instability, internal waves, geophysical and geological flows, stratified, flows
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 24 Apr 2019 08:06
Last Modified: 03 May 2019 10:21
URI: http://eprints.keele.ac.uk/id/eprint/6207

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