Journal
JOURNAL OF FLUID MECHANICS
Volume 863, Issue -, Pages 644-669Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2018.986
Keywords
chaos; chaotic advection; wakes
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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.
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