Characterizing coherent structures in Bose-Einstein condensates through dynamic-mode decomposition

We use the dynamic mode decomposition (DMD) methodology to study weakly turbulent flows in two-dimensional Bose-Einstein condensates modeled by a Gross-Pitaevskii equation subject to band-limited stochastic forcing. The forcing is balanced by the removal of energy at both ends of the energy spectrum through phenomenological hypoviscosity and hyperviscosity terms. Using different combinations of these parameters, we simulate three different regimes corresponding to weak-wave turbulence, and high- and low-frequency saturation. By extracting and ranking the primary DMD modes carrying the bulk of the energy, we are able to characterize the different regimes. In particular, the proposed DMD mode projection is able to seamlessly extract the vortices present in the condensate. This is achieved despite the fact that we do not use any phase information of the condensate as it is usually not directly available in realistic atomic BEC scenarios. Being model independent, this DMD methodology should be portable to other models and experiments involving complex flows. The DMD implementation could be used to elucidate different types of turbulent regimes as well as identifying and pinpointing the existence of delicate and hidden coherent structures within complex flows.