Statistical Problems Connected WITH Asymptotic Solutions of the One-dimensional Nonlinear Diffusion Equation.
MARYLAND UNIV COLLEGE PARK INST FOR FLUID DYNAMICS AND APPLIED MATHEMATICS
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The topic treated in the report is a distant outcome of old attempts to arrive at a statistical theory of turbulent fluid motion, modeled after the example of classical statistical mechanics as applied to the kinetic theory of gases. The attempts did not bring the desired success, but they made clear that essential features of the spectrum of turbulence are due to the simultaneous presence of dissipative as well as nonlinear inertial terms in the equations of motion. It seemed attractive therefore to study the interaction between these terms in an extremely simplified equation, the one-dimensional nonlinear, diffusion or heat flow equation U sub t uu sub x nu u sub xx. The study proved to have an interest of itself, and a set of results referring to asymptotic solutions, corresponding to vanishing viscosity and large values of t , is described in the report.
- Fluid Mechanics