March 22, 2017
March 22, 2017
Speaker: Anthony Leonard, Ph.D.
California Institue of Technology
Title: A New Look At The Linearized Navier-Stokes Equation
Location: Fiber Optics Building, Easton Hub Auditorium
Time: 3:30 p.m.
Abstract: In a number of recent investigations of wall-bounded flows, solutions to the linearized Navier-Stokes equations have played a major role. Such examples are the study of the origin and role of very large scale structures in the dynamics of turbulent pipe flow (McKeon & Sharma) and the development and application of low-complexity models to investigate the statistics of wall-bounded turbulent flows (Zare et. al). In both cases the authors had to undertake a significant computational effort to compute the resolvent of the Orr-Sommerfeld/Squire operator. In this talk we discuss the use of the WKB approximation on the linearized equations to construct analytically the Green's function for their solutions for the inviscid case in terms of the Bessel functions J1 and Y1, their modified counterparts, and the Airy functions Ai and Bi. Application to the case of plane Poiseuille flow reveals a narrow strip of high-amplitude solutions for the Green's function in the (kx, , kz ) plane including a one-dimensional family of homogeneous solutions to the inviscid equations with negative wave speeds.
Bio: Anthony Leonard is the Theodore von Kármán Professor of Aeronautics, Emeritus at the California Institute of Technology. He received a B.S. degree in Mechanical Engineering from Caltech in 1959 and a Ph.D. in Mechanical Engineering from Stanford in 1963 with a specialty in nuclear engineering. He had positions at the RAND and 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. For the past 32 years he has been at Caltech. He is a member of the US National Academy of Engineering, a Fellow of the American Physical Society, and a Life Member of Clare Hall, University of Cambridge. 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, techniques for large-eddy simulation, and low-order modeling of vortex flows. He has also been involved in the application of dynamical systems theory to fluid transport and mixing.
Richard Bruce Pelz (1957-2002) was Professor of Mechanical and Aerospace Engineering at Rutgers University, specializing in computational fluid dynamics. He received his Ph.D. from Princeton University in 1983, joined Rutgers as an assistant professor in 1986, and became full professor in 1998. Prof. Pelz was an expert in spectral methods and developed new parallel FFT algorithms for different parallel supercomputers, for example, receiving Honorable Mention in the competition for the Gordon Bell Award for Large Scale Scientific Computing in 1998. Prof. Pelz was deeply interested in the mathematical solutions to the equations of fluid dynamics and in particular the asymptotics and modeling required to join the computational with the analytical. He received international recognition for his work by being appointed as Regional Editor, Fluid Dynamics Research in 1996; Program Organizer, Isaac Newton Institute for Mathematical Sciences, Cambridge England; “Geometry and Topology of Fluid Flows” September December 2000, Co-organizer, NATO Advanced Science Institute for Mathematical Sciences, September 4 22, 2000; Co-organizer, Royal Society Discussion Meeting, “Topological Methods in the Physical Sciences,” London, November 15 16, 2000; Co-organizer, Conference on “Singularities in Classical, Quantum and Magnetic Fluids,” Warwick, October 20 23, 2000. During the last decade of his life, Prof. Pelz devoted much of his time to the blowup or singularity problem for the Euler and Navier-Stokes equations.
For additional information, please contact Professor Howon Lee at 848-445-2213 or at firstname.lastname@example.org.