Machine Learning Period-Doubling in Inertialess Viscoelastic Kolmogorov Flow

The flow of dilute polymer solutions can exhibit highly complex spatio-temporal chaos, even at vanishing inertia, a phenomenon commonly referred to as purely elastic turbulence. Curiously, however, the mechanism of transition to such dynamical states is thus far poorly understood, particularly in rectilinear geometries. Recently, it has been demonstrated that the inertialess Kolmogorov flow of an Oldroyd-B fluid can achieve elastic turbulence -- even in two dimensions -- following a series of period-doubling bifurcations driven by narwhal-like coherent structures in the elastic stress. Here, we attempt to construct low-dimensional models of this behavior, leveraging Sparse Identification of Nonlinear Dynamics (SiNDy) to reduce the flow trajectory to that described by a small set of energetically efficient POD modes. Similar approaches have also been adopted for extensional geometries, such as the canonical four-roll mill configuration. Our work has implications for low-order representations of non-Newtonian flow dynamics captured via machine learning techniques.