Hyperbolicity and Shadowing Directions of a Chaotic Developing 3-D Flow
Angxiu Ni · arXiv (Cornell University) · 2017
We demonstrate large developing chaotic systems' potential of satisfying the hyperbolicity assumption and having shadowing directions, using as an example compressible flow simulation of the 3-D cylinder flow at Reynolds number 525. We find that the first 40 CLVs are active at different locations in the wake region, indicating CLVs point to different directions, and the system being hyperbolic. Next, via the Non-Intrusive Least Squares Shadowing (NILSS) algorithm, we compute shadowing directions, which reveals how the statistics of the flow field respond to small parameter perturbations.