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

A.D. Neate and A. Truman

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0013
Subject:
Mathematics, Probability / Statistics, Analysis

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 ... More


Shocks

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0006
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

When the speed of a fluid exceeds that of sound, discontinuities in density occur, called shocks.The opposite limit from incompressibility (constant density) is constant pressure. In this limit, we ... More


Hamiltonian Systems Based on a Lie Algebra

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0010
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

There is a remarkable analogy between Euler’s equations for a rigid body and his equations for an ideal fluid. The unifying idea is that of a Lie algebra with an inner product, which is not ... More


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