Deformation of Material Lines and Surfaces in Chaotic Flows

Dr. Anthony Leonard
Professor of Aeronautics
Graduate Aeronautical Laboratories
California Institute of Technology

The deformation of material lines and surfaces as they evolve in a chaotic flow is considered. Of particular interest for the case of  a line are the curvature and torsion as a function of a\rclength along the curve. These quantities are sufficient to define the intrinsic geometry of the line. Regions of high curvature, once they start to develop, are essentially permanent, and in fact have a universal structure. Regions of high torsion, on the other hand, are transitory and correspond to a near singularity in the coordinate system of the Frenet frame rather than an exotic shape of the curve. In the case of a surface we attempt to characterize those portions that are in the vicinity of large principal curvature.

Anthony Leonard is the Theodore von Kármán Professor of Aeronautics at the California Institute of Technology. After receiving a B.S. degree in mechanical engineering at Caltech in 1959, he attended graduate school at Stanford University, receiving a Ph.D. in Mechanical Engineering in 1963 with a specialty in nuclear engineering. His research experience in a government/industrial setting includes three years at the RAND Corporation and twelve years at NASA’s Ames Research Center in the Computational Fluid Dynamics Branch. Dr. Leonard’s academic career includes seven years at Stanford as Assistant and Associate Professor of Mechanical Engineering and one year as Visiting Professor of Aeronautics at Caltech. For the past nineteen years he has been at Caltech.
Professor Leonard’s interests are in the area of computational fluid dynamics and its application to a wide variety of flows including turbulence, transitional flows, bluff-body aerodynamics, and flow-induced vibration. He has worked on developments in Lagrangian vortex methods, spectral methods, and in the technique of large-eddy simulation. He has also been involved in the application of dynamical systems theory to fluid transport and mixing.