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The unsteady motion of a gas–liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here, we explore the use of skeletonization to identify the minimum amount of information needed to describe their geometry. We skeletonize a periodic liquid jet by a modification of a recently introduced approach to coarsen multiphase flows while retaining a sharp interface. The process consists of diffusing an index function and at the same time moving the interfaces with it, until they “collapse” into each other and form skeletons. The skeleton represents the basic topology of the jet and we also keep track of how much the interface is moved (or how much volume is “accumulated”) during the process, which can be used to approximately reconstruct the jet. We explore various quantitative measures to characterize and distinguish the skeletons. These include standard morphometrics such as branch length distribution, after segmenting the skeletons into branches, and a more sophisticated representation of the skeleton structures called topology morphology descriptor, to obtain an “equivalent” description of the skeletons by retaining information about the topology in a compact way. 

Machine learning is used to develop closure terms for coarse grained model of two-dimensional turbulent flow directly from the coarse grained data by ensuring that the coarse-grained flow evolves in the correct way, with no need for the exact form of the filters or an explicit expression of the subgrid terms. The closure terms are calculated to match the time evolution of the coarse field and related to the average flow using a Neural Network with a relatively simple structure. The time dependent coarse grained flow field is generated by filtering fully resolved results and the predicted coarse field evolution agrees well with the filtered results in terms of instantaneous vorticity field in the short term and statistical quantities (energy spectrum, structure function and enstropy) in the long term, both for the flow used to learn the closure terms and for flows not used for the learning. This work shows the potential of using data-driven method to predict the time evolution of the large scales, in a complex situation where the closure terms may not have an explicit expression and the original fully resolved field is not available.