402 
In describing the motion of the water in the spherical shell 
between a(t) and R(t), it is convenient to use the Eulerian form of the 
hydrodynamical equations of continuity and motion. With the neglect of 
stresses arising from viscosity, these equations are: 
EN el pa eer ) 
D “— 
Leieee sy ib es, (3.1) 
> = eet a Ub" V; 
Eqs. 301 must be supplemented by the equation of state of the fluid, 
which provides a relation between pressure, density, and entropy, and 
the equation of entropy transport 
DiS webentiew! 
Dt 
where S is the specific entropy of the fluid (entropy per gram), The 
(3.2) 
entropy transport equation is based upon the assumption that the fluid 
experiences only reversible adiabatic changes of state behind the shock 
front, which is true if the influence of heat conduction and diffusion 
can be neglected in the time interval during which an element of fluid 
is traversed by the wave. At this point it is not assumed that all ele- 
ments of fluid are on the same adiabatic; and, indeed this is not strictly 
true, since at a shock front of changing intensity, the entropy increment 
of an element of fluid at the shock front depends upon the time at which 
it passes through the front. 
It is convenient to eliminate p and p from emiations 3,1 and 3,2 
with the introduction of the enthalpy or heat content H, defined as 
16 
