  Here, we provide a theoretical framework revealing that a steady compression
ramp flow must have the minimal dissipation of kinetic energy, and can be
demonstrated using the least action principle. For a given inflow Mach number
$M_{0}$ and ramp angle $\alpha$, the separation angle $\theta_{s}$ manifesting
flow system states can be determined based on this theory. Thus, both the
shapes of shock wave configurations and pressure peak $p_{peak}$ behind
reattachment shock waves are predictable. These theoretical predictions agree
excellently with both experimental data and numerical simulations, covering a
wide range of $M_{0}$ and $\alpha$. In addition, for a large separation, the
theory indicates that $\theta_{s}$ only depends on $M_{0}$ and $\alpha$, but is
independent of the Reynolds number $Re$ and wall temperature $T_{w}$. These
facts suggest that the proposed theoretical framework can be applied to other
flow systems dominated by shock waves, which are ubiquitous in aerospace
engineering.
