A&OS C115/C228 – Mountain waves

where N = g θ̄ dθ̄ dz was the Brunt-Vaisalla (BV) frequency and θ̄ = θ̄(z) was the potential temperature of the environment. For a stable environment (N > 0) we assumed a temporally varying solution of the form z′(t) = ẑe−iωt, where for period P , ω ≡ 2π P . Substitution of the assumed solution into (1) yielded ω = ±N , which means the parcel oscillation period is equal to the BV period of the environment.