1053 
THE DECAY OF PLANE, CYLINDRICAL AND 
SPHERICAL SHOCK WAVES 
A. J. Barris 
Road Research Laboratory, 
London 
September 1942 
* * * * * ** 
Summary. 
Exoressions are Jeducea connecting the rate cf decay of the pressure at a shock front in 
a soherical cylinarical or olane wave witn tne scace rates of change of oressure and particle 
velocity Dehing thexsnock front. it is sujyested that these may De used t derive some idea of 
the tnickness of a Shock wave when its rate of cropayation has been determined as a function of 
time. 
we sHall consider cnly the scnerical wave, since the olane wwe is merely a oarticular 
case of this mors -genoral tyoe, Taylor(1) has given an approximate exoression relating tne rate 
of decay to the stoce of tne wave immediately benind the shock front. The eres2nt analysis 
results in & more accurate ralation, morecver the cerresoonding results for soherical and 
cylinarical wayés given here are new. 
Assuming soherical symmetry in the wave we take spnerical co-ordinates with origin at 
the centre of the snock front. 
r = distance of coint from crigin of co-ordinates. 
t = time, 
u = oarticle velocity in direction cf r increasing. 
P = Gensity of yas. 
c = oressure in jas. 
ay "= cressure immediately behind shock front. 
ws, = velccity of oarticlss immediately Denino shock front. 
Dy = velocity of shock front, 
a Gensity of yas Dehing shock front. 
2 =. radius of shock front sohere at time t. 
Equations of mction ano continuity are 
Ou OL TS st ROK 
Eitan ike ayes (2) 
224 4 Dlr? py = 0 (2) 
Py 4, >, P, ana R are functions of t only and we have 
C) 2 
obus eee te fe} Ze ENp ou at eag (3) 
at =6Ot Sonn 
4p, Cy) ap 
——_ = ese + Db — t = F ) 
dt t 1 Or es (4) 
Gu, 3 u “ Cl) u i > 
Ko 2 Se Db = oe 
Athen Sten > 2 Omen (5) 
i} - ‘ fF 
Let By Jenote the rate of cnanue asscciateo witn a carticular jas varticls, i.e, 
abe. 2 
So 
al 
oy 
