2 research outputs found
Global generalized solutions for Maxwell-alpha and Euler-alpha equations
We study initial-boundary value problems for the Lagrangian averaged alpha
models for the equations of motion for the corotational Maxwell and inviscid
fluids in 2D and 3D. We show existence of (global in time) dissipative
solutions to these problems. We also discuss the idea of dissipative solution
in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit
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Self-Consistent Multiscale Theory of Internal Wave, Mean-Flow Interactions
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The research reported here produced new effective ways to solve multiscale problems in nonlinear fluid dynamics, such as turbulent flow and global ocean circulation. This was accomplished by first developing new methods for averaging over random or rapidly varying phases in nonlinear systems at multiple scales. We then used these methods to derive new equations for analyzing the mean behavior of fluctuation processes coupled self consistently to nonlinear fluid dynamics. This project extends a technology base relevant to a variety of multiscale problems in fluid dynamics of interest to the Laboratory and applies this technology to those problems. The project's theoretical and mathematical developments also help advance our understanding of the scientific principles underlying the control of complex behavior in fluid dynamical systems with strong spatial and temporal internal variability