ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

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 ). 501-517 .

[img] PDF
exact.pdf - Published Version
Restricted to Registered users only

Download (364Kb) | Request a copy
Official URL: http://www.jstor.org/stable/52515

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
Additional Information: Copyright of this article belongs to The Royal Society.
Department/Centre: Others
Date Deposited: 31 May 2011 09:08
Last Modified: 31 May 2011 09:08
URI: http://eprints.iisc.ernet.in/id/eprint/36456

Actions (login required)

View Item View Item