Page:Chandrasekhar - On the decay of plane shock waves.djvu/9

 $$dP=\frac{\partial P}{\partial x}\left[dx-(u+c)dt\right]+\frac{1}{\gamma-1}c^2\frac{\partial\log\theta}{\partial x}dt$$,

and

$$dQ=\frac{\partial Q}{\partial x}\left[dx-(u-c)dt\right]+\frac{1}{\gamma-1}c^2\frac{\partial\log\theta}{\partial x}dt$$,

where

and $$\theta$$ denotes the potential temperature (i.e., the temperature which the element of gas under consideration would have if reduced adiabatically to a certain standard pressure). For shocks of moderate Intensities the term in $$\theta$$ which, incorporates the changes in entropy can be ignored and we have

and

The foregoing equations are equivalent to

and

The particular significance of the case

is now apparent: Q has the value 5 outside the shock pulse, it retains its value (to within 1% for y ≤ 2.5) as we cross the shock. Moreover, according to equation (8) since