  This paper uses compressible flow simulation to analyze 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.
