On the Equilibrium Spectrum of Transient Waves in the Atmosphere

Abstract

The spectrum of transient heat flux in the midlatitude troposphere has a maximum at a synoptic scale. The same is true of the transient energy. The wavenumber of these maxima can be explained by the theory of nonlinear baroclinic adjustment, which is also shown to predict the shape of the spectra. According to this theory, each zonal wave has a nonlinear threshold that bounds its growth, and the bounds are larger for longer waves. The most unstable wave grows and transports heat until it reaches its threshold, at which point it breaks and saturates, passing off excess energy to the next longer wave. The process repeats, with energy cascading upscale, until the total heat transport is sufficient to reduce the meridional temperature gradient down to a relatively constant equilibrium level, independent of forcing. Thus at higher forcings more heat must be transported and the cascade extends to longer scales. At equilibrium, the longest heat-transporting wave has not saturated but rather has been rendered linearly neutral by the reduction in the temperature gradient. Observations from the real atmosphere, and computations with a quasigeostrophic two-level model in a beta-plane channel, corroborate the theory presented.