On converging shock waves of spherical and polyhedral form

380 D. W. Schwendeman
(a) Time = 0.2921 Average radius = 0.2378 (b) Time = 0.3021 Average radius = 0.2020
7
7
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6
Shock Mach number
5
4
Shock Mach number
5
4
3
3
(c) Time = 0.3069 Average radius = 0.1842 (d) Time = 0.3110 Average radius = 0.1679
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7
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Shock Mach number
5
4
Shock Mach number
5
4
3
3
(e) Time = 0.3147 Average radius = 0.1527 ( f ) Time = 0.3183 Average radius = 0.1376
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7
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Shock Mach number
5
4
Shock Mach number
5
4
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3
Figure 9 (a–f ). For caption see facing page.
with the behaviour of the local extrema in Mach number along the ray from V . If we
label the Mach number and radius at local maxima, say, as M p and r p , respectively,
then it is evident from the plots that
M p ∝ r −2/n
p
so that the increase in Mach number for each step of the repeating sequence follows