EXACT N-WAVE SOLUTIONS FOR THE NONPLANAR BURGERS-EQUATION

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, whe re m and n are positive integers with no common factors, is given. Thi s solution is asymptotic to the inviscid solution for Absolute value o f 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 asymptoti c 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, an d 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 a lternative approach for this case gives the large time behaviour in tw o different time regimes. The results of this study are compared with those of Crighton & Scott (1979).