Coherent Structure Visiometrics:From the Soliton to HEC
In this paper I give a brief personal review of the history of the early soliton days and how they led to the visiometrics and reduced modeling paradigm that has been a part of my approach to nonlinear science in the last three decades. I illustrate it with HEC (Hybrid Elliptic-Contour): a fast, minimal, asymptotically motivated model for unforced, 2-dimensional incompressible weakly dissipative turbulence (U2DIT).
Key wordsvisiometrics reduced modeling asymptotics fluid dynamics
Unable to display preview. Download preview PDF.
- 2.Bitz, F. J. and Zabusky, N. J.: David and ‘visiometrics’: Visualizing and quantifying evolving amorphous objects, Computers in Physics, Nov./Dec. (1990), 603–614.Google Scholar
- 4.Deem, G. S., Zabusky, N. J., and Kruskal, M. D.: Formation, propagation and interaction of ‘solitons’ in nonlinear dispersive media (numerical solutions of differential equations describing wave motion in nonlinear dispersive media), Bell Telephone Laboratories Film Library, 1965–1975.Google Scholar
- 6.Dritschel, D. G.: Vortex feature tracking in high reynolds number two-dimensional flows, in preparation, 1995.Google Scholar
- 9.Dritschel, D. G.: A general theory for two-dimensional vortex interaction, submitted to J. Fluid Mech., 1995.Google Scholar
- 11.Dritschel, D. G and Zabusky, N. J.: Toward a reduced model for nearly-inviscid unforced incompressible two-dimensional turbulence, letter submitted to Phys. Fluids, 1995.Google Scholar
- 17.Piva, R., Riccardi, G., and Benzi, R.: A physical model for merging in 2d decaying turbulence, Preprint, 1995.Google Scholar
- 19.Taub, A. (ed.): The Collected Works of John von Neumann, Macmillan, New York, 1963.Google Scholar
- 20.Yao, H. B., Dritschel, D. G., and Zabusky, N. J.: High-gradient phenomena in 2d vortex interaction, to appear in Phys. Fluids, 1995.Google Scholar
- 25.Zabusky, N. J., Silver, D., Pelz, R., and Vizgroup ’93: Visometrics, juxtaposition, and modeling, Phys. Today (1993), 24–31.Google Scholar