Theorem: for linear theta(z) = theta_0 + beta z, N^2 theta - g d theta/dz = 0 identically

Theorem (Brunt-Vaisala-linear-theta canonical): for linearly stratified atmosphere theta(z) = theta_0 + beta z with constant lapse rate beta, the Brunt-Vaisala definition N^2 = g * (d theta/dz) / theta gives N^2 (theta_0 + beta z) = g…