Exact N-Wave Solutions for the Non-Planar Burgers Equation

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
Publication:	Proceedings of the royal society a:mathematical,physical & engineering sciences
Publisher:	The Royal Society
Additional Information:	Copyright of this article belongs to The Royal Society.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
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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