Fluid dynamics of geometric rough flows
Abstract
We propose to develop a new methodology for uncertainty quantication and reduction of uncertainty in computational fluid dynamics by developing the theory of Geometric Rough Paths (GRP) based.in the foundations of transformation theory and multi time homogenisation for fluid dynamics. In our earlier results, the stochastic fluid velocity decomposition results show that the principles of transformation theory and multi time homogenisation enable a physically meaningful, data driven and mathematically based approach for decomposing the fluid transport velocity into its drift and stochastic parts. This approach can be applied immediately to the class of continuum flows whose deterministic motion is based on fundamental variational principles. We expect that extending our stochastic modelling approach to the realm of Geometric Rough Paths will be effective whenever a body of hydrodynamic transport data shows the characteristic signal of high power at low frequencies. This characteristic signal is often seen in flows in Nature, such as atmospheric and oceanic geophysical flows, and in three dimensional fluid turbulence in general. In such flows, the opportunity arises to decompose the corresponding Lagrangian trajectories into its fast and slow, or resolvable and unresolvable, components and extend our stochastic modelling experience to the realm of rough flows described here as a basis for quantifying a priori uncertainty and then using data assimilation methods (e.g., particle ltering) for reducing the uncertainty.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 14, 2022
- Source ID
- FA95501917043
Entities
People
- Darryl D. Holm
Organizations
- Air Force Office of Scientific Research
- Imperial College London
- United States Air Force