Polytropic-coefficient function (PCF) VS. polytropic-exponent function (PEF)

Summary form only given. In fluid treatments of plasma-wall-transition (PWT) problems, the system of fluid equations of a given particle species is often¹⁻³ closed by means of an equation of the form Dp/Dt = (γp/n) Dn/Dt (“local polytropic law”), where n(x⃗, t) and p(x⃗,t) are the density and pressure, γ(⃗x,t) is called the “polytropic-coefficient function (PCF)”3, and D/Dt = ∂/∂t + ⃗u · ∇ is the Lagrangian time derivative for a “streaming” point observer, i.e., an observer moving along with a fluid “particle” in the flow-velocity field ⃗u (⃗x,t).