On the theory of large‐scale disturbances in a two‐dimensional baroclinic equivalent of the atmosphere

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Abstract
The equations of non‐viscous, adiabatic flow have been reformulated to apply to a two‐dimensional equivalent of a three‐dimensional baroclinic fluid. The state of this ‘equivalent‐baroclinic’ fluid is to be identified with conditions at a definable ‘level of equivalence’ in the true atmosphere. The two equations of equivalent‐baroclinic flow, in which neither vertical motions nor vertical dependence enter explicitly, involve only two dependent variables ‐ the temperature and height of an isobaric surface. Since those equations form a closed system, they constitute a mathematically complete theory of the development and movement of large‐scale disturbances at the level of equivalence. The stability criterion for a special type of flow, previously studied by Fjörtoft and others, has been derived from the theory and compared with Fjörtoft's earlier results. This comparison shows that the stability characteristics of three‐dimensional baroclinic flow are reproduced in two‐dimensional equivalent‐baroclinic flow, and, accordingly, that the present theory allows for the development of disturbances once they are initiated. An iterative scheme, based on successive calculations of the temperature and height tendencies, has been proposed for solving the general non‐linear equations of equivalent‐baroclinic flow. This method provides the basis for a new technique of numerical weather prediction.