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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—such as Clebsch components—compared 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. We validate the Clebsch PFM method through a wide range of benchmark tests and simulation examples, ranging from leapfrogging vortex rings and vortex reconnections to Kelvin-Helmholtz instabilities, demonstrating that our method outperforms its impulse- or vortex-based counterparts on particle flow maps, particularly in preserving and evolving small-scale features.
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Generalized Clebsch Variables for Compressible Ideal Fluids: Initial Conditions and Approximations of the Hamiltonian
Clebsch variables provide a canonical representation of ideal flows that is, in practice, difficult to handle: while the velocity field is a function of the Clebsch variables and their gradients, constructing the Clebsch variables from the velocity field is not trivial. We introduce an extended set of Clebsch variables that circumvents this problem. We apply this method to a compressible, chemically inhomogeneous, and rotating ideal fluid in a gravity field. A second difficulty, the secular growth of canonical variables even for stationary states of stratified fluids, makes expansions of the Hamiltonian in Clebsch variables problematic. We give a canonical transformation that associates a stationary state of the canonical variables with the stationary state of the fluid; the new set of variables permits canonical approximations of the dynamics. We apply this to a compressible stratified ideal fluid with the aim to facilitate forthcoming studies of wave turbulence of internal waves.
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- Award ID(s):
- 2009418
- PAR ID:
- 10411239
- Date Published:
- Journal Name:
- Fluids
- Volume:
- 7
- Issue:
- 4
- ISSN:
- 2311-5521
- Page Range / eLocation ID:
- 122
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/fluids7040122
