This Project Grant award for $257,457 from the National Science Foundation (NSF) Division of Mathematical Sciences supports research by the University of Alabama at Birmingham (UAB) to investigate three key problems in fluid mechanics. The overarching objective is to utilize a novel mathematical framework developed by the Principal Investigator to study the spatial intermittency of turbulent flows, which is critical for understanding phenomena like vortex structures in turbulence. The three subprojects aim to:
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Demonstrate how locality of nonlinear interactions implies regularity in the context of hyper-diffusion, which has implications for the physics of turbulence.
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Gain a logarithmic improvement in large data regularity results for Navier-Stokes flows by reformulating concepts of local one-dimensional sparsity.
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Investigate a stabilizing effect of viscosity on the classical vortex sheet roll-up problem through analyzing local one-dimensional sparsity of vorticity.
This award supports the NSF's mission to strengthen the nation's scientific enterprise through mathematical and physical sciences research, and has been deemed worthy of funding based on intellectual merit and broader impacts.
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