A new method that evaluates dominant local dynamics by skeletonization, mathematical term decomposition and the re-combination of a reduced number of dominant terms around the skeleton points is proposed to clarify the dynamics of hairpin vortices generated during the boundary-layer transition under free-stream turbulence (FST). The development of the method is based on the results of direct numerical simulations conducted for the laminar-turbulent transition on a flat plate with FST intensities of 0-6% and a free-stream Mach number of 0.5. Regarding the skeletonization, a new algorithm for extracting the interior points of vortex structures represented by enclosed iso-surfaces is developed. To identify the dominant terms, governing equations are decomposed into non-further-decomposable (NFD) terms. The proposed method is also extended to time series flow field data to reveal the variation of the combination set of dominant NFD terms during the evolution of vortex structures. The present method enables the automatic finding and categorization of the variations of the sets of dominant terms that govern local dynamics during the evolution of hairpin vortices.
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