MPS-LN 2002-11
August 2002

Lectures on Multiscale and Multiplicative Processes in Fluid Flows

by:

Ed Waymire et al

Abstract

These lecture notes were prepared for the Instructional and Research Workshop on Multiplicative Processes and Fluid Flows at MaPhySto, Aarhus University, 23-28 August 2001. Much of this is based upon collaborations within the Focussed Research Group on Navier-Stokes equations at Oregon State University/Indiana University on the one hand and the turbulence research group around Max-Planck Institute for Physics of Complex Systems, Dresden, on the other. In particular, the treatment of multiplicative Fourier cascade solutions to diffusion, fractional diffusion, reaction-diffusion, Burgers, and Navier-Stokes are largely un-published results due to the OSU/Indiana Focussed Research Group. Also included are results of long time collaborations with Vijay Gupta at University of Colorado on problems concerning hydrologic flows in ungauged river basins.

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This paper has now been published in Trans. Amer. Math. Soc. (2003) and in: Probability, Statistics and their Applications, Papers in honor of Rabi Bhattacharya, eds K. Athreya, M. Majumdar, M. Puri, E. Waymire, IMS Lecture Notes-Monograph Series, 65-80 (2002)