Some simple analytical solutions to the problem of forced equatorial long waves

This paper describes some simple time‐dependent analytical solutions to the problem of a sudden ‘switch‐on’ of heating localized about the equator. The equations used are the shallow water equations on the β plane under the ‘long wave approximation’. It is shown that, with a reasonable amount of dissipation, it can take several days for a steady state response to be established. In the early stages, the circulation differs considerably from that of the steady state. The long time scale for the adjustment process has implications in numerical weather prediction since it implies that if the initial data are not in balance with the model's forcing, it may take several days for a balance to be established, by which time the quasi‐stationary tropical flow may have been irrevocably changed.