Symmetry, Singularity, and Stability in Fluids and Plasmas

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The project is aimed at the study of nonlinear phenomena in fluids and plasmas that are of mathematical interest and of physical and engineering importance. They include cavitation, jet pinch-off and drop formation under the influence of surface tension, viscosity, and electrical fields, in compressible and incompressible fluids. The project is also concerned with singular thermal plume interactions with multiscale flows. Dynamics near multiscale equilibria of incompressible fluid equations with complex structured symmetry and the construction and confinement properties of quasisymmetric plasma equilibria are a second component of the project. These issues are relevant to plasma fusion confinement. The project will also provide opportunities for the involvement of graduate students in the research.One of the main areas of the project concerns topological change in two phase fluids and singularity formation in fluid interfaces. Physical experimental and numerical evidence show that surface tension and electrical forces can produce instability and finite time pinch-off of slender fluid jets. Surface tension may rupture thin threads connecting fluid cells embedded in another fluid. Advances in nonlocal and nonlinear analysis, coupled with geometric analysis are going to be developed to study these singular events. Thermal plumes play an important role in turbulent convection and are relevant to geophysics. The dynamics of thermal plume interactions will require the use of methods of analysis involving the interplay of singular integral and Lagrangian points of view. The construction of magnetostatic equilibria with nontrivial quasisymmetry involves geometrical and nonlinear PDE methods. The investigation of the confinement properties of these equilibria involves studies of inhomogeneous kinetic models with very singular coefficients.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.