Exact n-wave solutions for the non-planar Burgers equation

Sachdev, P. L. ; Joseph, K.T. ; Nair, K. R. C. (1994) Exact n-wave solutions for the non-planar Burgers equation Proceedings of the Royal Society of London Series A: Mathematical, Physical & Engineering Sciences, 445 (1925). pp. 501-517. ISSN 0962-8444

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Official URL: http://rspa.royalsocietypublishing.org/content/445...

Related URL: http://dx.doi.org/10.1098/rspa.1994.0074

Abstract

An exact representation of N-wave solutions for the non-planar Burgers equation ut + uux + ½ju/t = ½δ uxx, 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 |x| < surd (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, ½ , 1/3 and ¼. 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:Article
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ID Code:14845
Deposited On:12 Nov 2010 13:29
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