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Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow

Published online by Cambridge University Press:  28 January 2019

Angxiu Ni Open the ORCID record for Angxiu Ni [Opens in a new window]
Angxiu Ni*
Affiliation:
Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, USA
*
†Email address for correspondence: niangxiu@gmail.com
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Abstract

This paper uses compressible flow simulation to analyse the hyperbolicity, shadowing directions and sensitivities of a weakly turbulent three-dimensional cylinder flow at Reynolds number 525 and Mach number 0.1. By computing the first 40 covariant Lyapunov vectors (CLVs), we find that unstable CLVs are active in the near-wake region, whereas stable CLVs are active in the far-wake region. This phenomenon is related to hyperbolicity since it shows that CLVs point to different directions; it also suggests that for open flows there is a large fraction of CLVs that are stable. However, due to the extra neutral CLV and the occasional tangencies between CLVs, our system is not uniform hyperbolic. By the non-intrusive least-squares shadowing (NILSS) algorithm, we compute shadowing directions and sensitivities of long-time-averaged objectives. Our results suggest that shadowing methods may be valid for general chaotic fluid problems.

JFM classification

Nonlinear Dynamical Systems: Chaos Mixing: Chaotic advection Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 644 - 669
Copyright
© 2019 Cambridge University Press 

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