Translation and Development in Two Dimensional Fields with Special Reference to Pressure Variations

Abstract

In previous studies of translation of field entities attention has been focused on singular points and lines of the field, with the result that the complementary concept of development in the field has been left either not at all, or quite arbitrarily, defined. By determining the least-squares fit to the rate of change of the entity throughout the field, rigid and unique definitions are derived of both the translation and rotation of the system of isolines of the entity, and also of the local and total development in the field. The practical result is to derive a system of weighting factors for the translation of elements of the field, and to stress the special importance of those regions where the gradient of the entity is greatest. In meteorology this means that the movement of pressure-systems is dominated by that of the regions of strongest wind. Comparison is made with earlier results, and the question of the consistent motion of coexistent fields (e.g. pressure and temperature) is discussed.