Burgers-KPZ Turbulence: Göttingen Lectures

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. Howev...

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Bibliographic Details
Main Author: Woyczynski, Wojbor A
Format: Book
Language:English
Subjects:
Burgers equation
Differential equations, Parabolic
Differential equations, partial
Distribution (Probability theory
Interfaces (Physical sciences)
Mathematics
Mathematics and Statistics
Partial Differential Equations
Probability Theory and Stochastic Processes
Turbulence
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Summary:These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0093107