Theorem: omega k_x + beta = 0 at k_y = 0, L_d -> inf (barotropic Rossby westward)

Theorem (Rossby-westward canonical): in the barotropic limit (L_d -> infinity, no stratification effect) and zonal wavenumber only (k_y = 0), the Rossby dispersion omega = -beta k_x/(k_x^2) = -beta/k_x. Cleared: omega k_x = -beta, residual…