 Stagnation temperature

The temperature reached by bringing a flow to rest adiabatically while converting its kinetic energy to enthalpy. For a calorically perfect gas, $T_{\mathrm{stag}}=T+u^2/(2c_p)=T[1+(\gamma -1)M^2/2]$. It is conserved across an adiabatic normal shock even though entropy increases and stagnation pressure decreases.