Sachdev, PL and Joseph, KT and Nair, KRC
(1994)
*Exact N-Wave Solutions for the Non-Planar Burgers Equation.*
In: Proceedings of the royal society a:mathematical,physical & engineering sciences, 445
(1925).
pp. 501-517.

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## Abstract

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).

Item Type: | Journal Article |
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Additional Information: | Copyright of this article belongs to The Royal Society. |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | Ms V Mangala |

Date Deposited: | 31 May 2011 09:08 |

Last Modified: | 16 Oct 2018 07:23 |

URI: | http://eprints.iisc.ac.in/id/eprint/36456 |

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