Hydrostatic-Balance

Isentropic base-state atmosphere for the Clark (1977) terrain-following mountain-wave model, "A Small-Scale Dynamic Model Using a Terrain-Following Coordinate Transformation", Eqs. 2.6-2.9. The base state assumes a constant potential temperature Θ — the deep, isentropic reference atmosphere of Ogura and Phillips (1962) adopted in Clark (1977) Eq. 2.6 — and derives the height-dependent thermodynamic profiles that satisfy hydrostatic balance: from the reference potential temperature Θ, the surface pressure P_0, and the height above the surface z, the component computes the isentropic scale height H_s = c_p*Θ/g, the base-state temperature T_bar = Θ*(1 - z/H_s) (Eq. 2.7), the base-state pressure p_bar = P_0*(1 - z/H_s)^(c_p/R_d) (Eq. 2.8), and the base-state density ρ_bar = P_0/(R_d*Θ)*(1 - z/H_s)^(c_p/R_d - 1) (Eq. 2.9). Temperature falls linearly with height while pressure and density fall as powers of the same (1 - z/H_s) factor, all three vanishing at the top of the isentropic atmosphere z = H_s. Four purely-algebraic equations, no time integration. Migrated from AtmosphericDynamics.jl@816cc391 src/clark1977.jl:49 (`IsentropicBaseState` @component); the five upstream @constants — g, R_d, c_p and the derived exponents inv_kappa = c_p/R_d and inv_kappa_m1 = c_p/R_d - 1 — are declared as fixed-default parameters.