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Abstract
The main purpose of this investigation is to examine to what extent large-scale heat sources are responsible for the formation and behaviour of ultra-long waves in the atmosphere. This has been performed with the aid of a linear, time-dependent, quasigeostrophic model in which non-adiabatic heating has been assumed to be proportional to the temperature difference between the atmosphere and the underlying surface.
Results obtained with this model exhibit certain characteristic features which are in agreement with observational studies of these long waves in middle latitudes during winter.
Thus the solution consists of a stationary part and a travelling part. For the lowest longitudinal wave-numbers the stationary part is very close to the observed mean conditions in the lower part of the atmosphere.
The non-stationary part consists of two travelling waves which have decaying amplitudes for the three lowest wave numbers; in the corresponding adiabatic case the solution is amplifying.
The phase-velocity for the wave-component which decays most slowly is close to the Rossby phase velocity modified by a weak divergence effect.
If the initial condition is chosen so that the system is not in thermal equilibrium, the resulting motions of the ultra-long waves are slowly damped fluctuations about a mean state.