Mesh-free resolvent analysis for operator-based discovery of large-scale coherent structures: implementation and the example of the stratified wake behind a sphere

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Flow instabilities and large-scale coherent structures (e.g. vortices) often lead to faster heating and unwanted drag on aerospace vehicles and can be inherent in the formation of weather events such as tropical cyclones. Predictive physics-based modeling tools for large-scale coherent structures in turbulent flows are needed in computational aeroscience, natural science, and environmental engineering. Novel numerical approaches will be developed to better simulate technical and natural turbulent flows in three-dimensional complex geometries. The goal of the dissemination strategy is to make the numerical tools developed in this project freely accessible to researchers from diverse backgrounds and disciplinary areas. In addition, the new tool will be used in graduate level courses.This research identifies an opportunity to facilitate high-order accurate resolvent analyses of complex flows as they occur in nature and in engineering. A key-enabler for the proposed methodology is a recent break-through in the computation of mesh-free radial basis function discretization. In contrast to methods that approximate the discrete Jacobian from residual evaluations, the proposed method permits the adjustment of the accuracy of the discretization to arbitrarily high order, uses a mesh-free approach that significantly simplifies the discretization of complex domains and local grid refinement, and works as a stand-alone tool that can be applied to flow data from different numerical or experimental sources. To demonstrate the capabilities of the developed technology, the project investigates the wake flow behind bluff bodies in density-stratified flows. Motivated by the theoretical correspondence between operator-based resolvent modes and empirical modes computed using spectral proper orthogonal decomposition, the research conducts a comparative study of stratified wake physics using both methods.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.