A systematic search of turbulence for periodic orbits with automatic differentiation

  • Page, Jacob (University of Edinburgh)

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In this talk I will discuss a new approach in the search for turbulent periodic orbits based on automatic differentiation that appears to dramatically overcome past limitations, using two-dimensional Kolmogorov flow as an example. By using a fully-differentiable flow solver and an appropriate loss function, robust guesses for UPOs with specific properties can be generated via a gradient descent algorithm, before being converged with a few iterations of standard Newton solver. I will use the new method to examine the distribution of periods in a weakly turbulent system before converging hundreds of new solutions in a strongly turbulent flow, where < 10 solutions have been found by previous methods. I will discuss the various physical processes captured in the collection and attempt to estimate flow statistics in an approach inspired by periodic orbit theory.