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On the theory of large‐scale vortex motion in the atmosphere
Author(s) -
James R. W.
Publication year - 1950
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49707632902
Subject(s) - vortex , geostrophic wind , kinetic energy , physics , dimensionless quantity , cyclone (programming language) , mechanics , classical mechanics , meteorology , field programmable gate array , computer science , computer hardware
A consideration of the parameters best suited to characterising a circular vortex leads to the conclusion that an intensity factor, the central pressure defect (or excess) and a scale, or size factor are fundamental. General expressions are given for the mass defect of a cyclone, its total potential energy, and the total kinetic energy of geostrophic winds. These parameters are estimated for 17 cyclones on the basis of an assumed pressure‐profile shape. It is shown that the ratio of the mean geostrophic kinetic energy to the mean potential energy is of the order 0.08. A dimensionless measure of the‘flexure’ or bending of a pressure profile is shown to vary relatively slightly from cyclone to cyclone, suggesting that the profile shape is roughly the same for all symmetrical lows. The kinetic energy arising from ageostrophic components of wind are also discussed and it is shown that a quasi‐geostrophic vortex in bodily movement has the same (ageostrophic) kinetic energy as a rigid body moving with the same speed and having a specified mass, the virtual mass of the vortex. It is shown that the virtual mass of a cyclone is of the same order as the total mass defect. It is shown how elleptical vortices, troughs and wedges may be treated, and a‘front’ is shown formally to be representable as a line distribution of circular vortices. On the basis of the models introduced, a dynamic theory of quasi‐geostrophic vortex interaction is put forward, based on the hypothesis that in mutual interaction the pressure profiles of individual vortices are conserved. This theory leads to the conception of a potential barrier inhibiting the over‐close approach of two vortices, and permits vortex interaction to be conceived as the motion of attracting and repelling'centres of action.