Identifying Locally Turbulent Vortices within Instabilities

This work presents an approach for the automatic detection of locally turbulent vortices within turbulent 2D flows such as instabilites. First, given a time step of the flow, methods from Topological Data Analysis (TDA) are leveraged to extract the geometry of the vortices. Specifically, the enstrophy of the flow is simplified by topological persistence, and the vortices are extracted by collecting the basins of the simplified enstrophy's Morse complex. Next, the local kinetic energy power spectrum is computed for each vortex. We introduce a set of indicators based on the kinetic energy power spectrum to estimate the correlation between the vortex's behavior and that of an idealized turbulent vortex. Our preliminary experiments show the relevance of these indicators for distinguishing vortices which are turbulent from those which have not yet reached a turbulent state and thus known as laminar.

Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the L2 norm) and (ii) an established topological distance between persistence diagrams (the L2-Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.