Cooling across an isothermal shock (${\mathcal{L}}_A=j(u_1^2-u_2^2)/2$)

The specific enthalpy is equal on both sides of an isothermal perfect-gas shock. The energy removed per unit area per unit time is $j(u_1^2-u_2^2)/2$, with $j>0$ the normal mass flux. Net cooling therefore selects compression shocks; an expansion jump requires heating.