Perturbations About Strong Spherical Shock Waves

Cover Perturbations About Strong Spherical Shock Waves
Perturbations About Strong Spherical Shock Waves
Cathleen Morawetz
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'S^ nr. -= ;C' '!■-; i':' ' ■" J ^ .
. U -, 1. _. -. , .. , . , .
• .. E. ' ' ' ^. \ ■: \ '«'-■■-• -^ •' , . '-'1 . \ •■^-. R. I .. I\ \ T: ) t i ;. >. \ \ . R : !
1 ;* ) ' r 1 -'T-; ■rf. '-, t' Substituting (39) and ([lO) in (38) and tbon (37) we find t^iat h = -3J. 1. 938 and finally, from (27), (^1) n^ = t°/^i. 3553(7f) -. 3697 (jf-) > ■\{ /w N-^-. 600( / ^. 1^738 /^ xO. 32121 C-L = r J -1. 61^2 (JLj +. 8323(J-j +1. 8326^^] j Pi = r^J -2. 1, 662 (^|Lj +i. 92[, 2(|Ly +L|.. L:. 369(f ■) V H^ -
... -3. I]-938 t^/-'' .
In Figures 1, 2 and. 3 wo have plotted the path of the shock as a function of tirae and the maximum pressure as a function of time and distance.
^ '^ ^. Behind a Do tona t i on .
The third shock condition in (12) miist bo modified to include the chomical energy of the cctoaation. VJo then have for the conditions across the front (1|. 2) p(u-z) = - p-|^z 2 2 p(u-z) + p = p z -;- p^ n p — 2 YP-i — P(y-1) 2' 2 p^(y^-1; 1 vjhcre E and E, are the energy of formation per unit mass of the burnt and unburnt material respectively, and y..


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