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Graph."],"published-print":{"date-parts":[[2025,8,1]]},"abstract":"<jats:p>We propose a novel gauge fluid solver that evolves Clebsch wave functions on particle flow maps (PFMs). The key insight underlying our work is that particle flow maps exhibit superior performance in transporting point elements\u2014such as Clebsch components\u2014compared to line and surface elements, which were the focus of previous methods relying on impulse and vortex gauge variables for flow maps. Our Clebsch PFM method incorporates three main contributions: a novel gauge transformation enabling accurate transport of wave functions on particle flow maps, an enhanced velocity reconstruction method for coarse grids, and a PFM-based simulation framework designed to better preserve fine-scale flow structures. 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