Mechanics, thermodynamics, and radiative transfer of planetary atmospheres, with primary reference to Earth's troposphere and stratosphere. Hydrostatic balance — for a thin, stably-stratified atmosphere in local thermodynamic equilibrium,…
atmospheric-physics
Barometric formula: p(z) = p₀·exp(−z/H), H = k_B T/(m g)
Hydrostatic balance dp/dz = −ρg combined with the ideal-gas equation of state p = ρ·k_B T/m (m = mean molecular mass) gives a first-order…
Dry adiabatic lapse rate Γ_d = g/c_p ≈ 9.8 K/km
Adiabatic (dQ=0) displacement of an unsaturated air parcel through a hydrostatic atmosphere conserves specific entropy; rewriting the first…
Potential temperature θ = T·(p₀/p)^(R/c_p) (adiabatic invariant)
Potential temperature θ is the temperature a parcel would attain if brought adiabatically from its actual pressure p to a reference…
At z = H: p(H)/p₀ = e⁻¹ exactly
Closed-form evaluation of the barometric profile at its own scale height. Pressure ratio at z = H: p(H)/p₀ = exp(−H/H) = e⁻¹ (canonical…
Γ_d rational: 196133/20100000 K/m (g=9.80665, c_p=1005)
Closed-form rational evaluation of the dry adiabatic lapse rate using standard-gravity g = 9.80665 m/s² (2019 CIPM, BIPM SI Brochure 9th…
Adiabat: θ/T − (p₀/p)^κ ≡ 0 symbolically
Closed-form symbolic identity for the potential temperature. θ = T·(p₀/p)^κ; residual sp.simplify(θ/T − (p₀/p)^κ) = 0 exactly — a literal…