788 RV GHA RD SiO iN; 
TaBLE I. U—co/co, u, and AH in low pressure region 
(based on Ekman equation-of-state). Sea water: Initial 
temperature 15°C; salinity 32 parts per thousand (3.79 
wt. percent NaCl); co=4922.8 ft/sec = 1500.5 m/sec. 
A B 
U —co u AH U —co u AH 
t—Po co (m/ (cal/ p—po co (ft / (cal/ 
(kbar)  (%) sec) gm) (Ib /in?) (%) sec) gm) 
0.00 0.00 0.0 0.0 0 0.00 0.0 0.0 
.25 2.07 aly! 5.8 2,000 1.14 29.1 3.2 
50 4.03 31.2 11.5 4,000 2.27 57.6 6.4 
.75 5.93 46,2 iene 6,000 3.35 85.5 9.6 
199 7.81 60.5 23.0 8,000 4,43 112.9 12.7 
1.25 9.65 74.4 28.5 10,000 5.48 139.7 15.9 
1.50 11.44 87.7 34.1 12,000 6.53 166.0 19.0 
14,000 7.56 191.8 22.1 
16,000 8.58 217.1 25.2 
18,000 9.59 242.0 28.3 
20,000 10.57 266.5 31.4 
22,000 11.55 290.6 34.5 
TaBLE II. U—co/co, u, and AH in intermediate pressure 
region (1.5 to 25 kilobars) (based on Tait equation-of- 
state; 7=7.800, B =3.012). Sea water: Initial temperature 
25°C; salinity 32 parts per thousand (3.79 wt. percent 
NaCl): co=5014.7 ft/sec= 1528.5 m/sec. 
A B 
U —co u AH U —co u AH 
p—po co (m/ (cal/ p—DPo co (ft / (cal/ 
(kbar) (%) sec) gm) (b/in?) (%) sec) gm) 
0.0 0.00 0.0 0.0 0.0 0 0.0 
1.0 8.18 59.2 23.0 20,000 11.0 258 Sis 
1.5 11.88 85.5 34.2 30,000 15.8 375 46.6 
2.0 15.39 110.1 45.3 40,000 20.5 483 62.0 
2.5 18.71 135.0 56.3 50,000 24.7 584 77.0 
3.0 21.88 157.8 67.2 60,000 28.7 676 92.0 
4.0 27.84 200.5 88.8 70,000 32.5 767 107.0 
5.0 33.39 240.2 110.1 80,000 36.0 853 121.0 
6.0 38.59 277.5 131.2 90,000 39.4 937 135.0 
8.0 48.13 346.1 172.9 100,000. 42.8 1014 150.0 
10.0 56.73 408.9 214.0 120,000 49,2 1168 178.0 
12.0 64.70 466.9 254.8 140,000 55.2 1312 207.0 
14.0 72.25 510.9 295.2 160,000 60.8 1445 235.0 
25.0 108.40 709.1 514.4 180,000 66.3 1564 263.0 
200,000 71.5 1662 291.0 
value of AT is used in evaluating the right-hand 
side giving a more accurate value of AT on the 
left-hand side, and the process is repeated until 
the results of two successive steps differ by a 
sufficiently small amount. One or two steps 
generally suffice. 
We have thus obtained T as a function of p 
along the Hugoniot curve (see Fig. 1). It is now 
possible to calculate immediately the particle 
velocity u, the propagation velocity U, and the 
specific volume v as functions of p behind the 
shock front. The results using the Ekman 
equation-of-state and the Tait equation-of-state 
are tabulated in Tables I and II, respectively, of 
Section ITI. 
b. The Calculations of Richardson and Kirkwood 
Here we outline the calculations® intended for 
the applications of the shock wave propagation 
ARONS, 
AND HALVERSON 
theory of Kirkwood and Bethe.” These are based 
upon the equation-of-state and specific heat 
data discussed in detail in Appendix II. We 
use a modified Tait equation-of-state connecting 
v(p, T) and v(0, 7) to be discussed below. In 
most respects, the data is made to fit the proper- 
ties of an aqueous 0.7 molal NaCl solution 
assumed to be roughly equivalent to sea water 
of salinity s=32 parts per thousand (see Section 
1 of Appendix 1). 
In these calculations the initial pressure po is 
taken to be zero, and several different initial 
temperatures JT» are used: 0°C, 20°C, and 40°C. 
Before indicating the precise nature of the 
modification of the Tait equation, it is desirable 
to mention that in this part two different pairs 
of independent variables will be used: pressure 
and temperature (p,7), and pressure and 
entropy [p,S]. Consequently, in order to 
indicate which pair are used in a function, we will 
use parenthesis to indicate the first pair and 
square brackets to indicate the second, 1.e. 
v(p, T) and o[p, S]. 
The modified form of Tait equation introduced 
by Kirkwood? ® is 
log(v1/v) = (1/n) log(1+p/ALS]), 
where 
v=o[p, S]=v(, TLp, S}), u=2[0, SI, 
(see Fig. 1) 2 is an empirical constant, and the 
function A[.S] is related to the function B(¢) in 
the original isothermal form of the Tait equa- 
tion, Eq. (2.7), as follows, 
A[S]=B([0, S]), #=(1—273.16)°C.. (2.13) 
The reasons for introducing this modification of 
the Tait equation are at least twofold: (1) the 
anomaly of a vanishing specific volume u(p, 7) at 
a finite pressure along a given adiabatic (which 
does not differ markedly from the Hugoniot curve 
in the case of water) is removed to a higher pres- 
sure by replacing [v(0, 7) —v(p, T) ]/[v(0, T) ] 
TABLE III. Values of U—co/co for different temperatures 
and salinities at a shock wave peak pressure of 1.00 
kilobar. 
(2.12) 
Salinity Temperature U —co/co 
(parts per 1000) (°C) (%) 
32 15 7.81 
32 25 7.81 
35 15 7.76 
