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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics

On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics

Chapter:
(p.281) 13 On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

A.D. Neate

A. Truman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0013

This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. It shows that for small viscosities there exists a vortex filament structure near to the Maxwell set. It is discussed how this vorticity is directly related to the adhesion model for the evolution of the early universe, and new explicit formulas for the distribution of mass within the shock are included.

Keywords:   stochastic Burgers equation, caustic, Maxwell set, Hamilton-Jacobi level surface, stochastic turbulence, astrophysics, adhesion model

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