Abstract
The angular momentum of the atmosphere is the sum of the wind term, W, due to the winds relative to the earth's surface, and the matter term, M. It is shown that if the earth were an oblate spheroid with an equipotential surface, the atmospheric torque on the earth would be ‐Ω ∧ M, Ω being the rotation rate of the solid earth. As a result, the equatorial components of M for a wave propagating at azimuthal angular velocity σ without changing shape are (Ω ‐ σ)/Ω times the equatorial components of W. Laplace's equation for tidal motions ‘on a sphere’ strictly applies to motions on such an oblate spheroid and its solutions apply a torque on the earth equal to ‐Ω ∧ M. It is shown that the resulting relationship between M and W also implies that in any separable wave solution of the tidal equations the surface wind is simply related to the vertical integral of the wind and the equivalent depth.
Analyses of the equatorial components of the matter term by the weather forecast systems of the European Centre for Medium‐range Weather Forecasts and the Meteorological Office are dominated by chaotic oscillations with periods of between 8 and 10 days that are well forecast out to 5 days ahead. It is argued that these are essentially free solutions of the tidal equations which exert considerable torques on the earth. The main feature of the equatorial components of the wind term is a seasonally modulated diurnal oscillation. Analyses and 2‐day forecasts of this phenomenon are in less good agreement. It is argued that it is thermally forced and depends on the compressibility of the atmosphere.