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On the symmetric circulation of a moving hurricane
Author(s) -
Smith Roger K.,
Weber Harry C.,
Kraus Annette
Publication year - 1995
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.49712152412
Subject(s) - vorticity , physics , vortex , potential vorticity , vortex stretching , circulation (fluid dynamics) , barotropic fluid , burgers vortex , rossby wave , vorticity equation , mechanics , classical mechanics , atmospheric sciences
The evolution of the symmetric circulation of a moving hurricane‐scale vortex on a beta‐plane is investigated and interpretations of this investigation are given in terms of vorticity fluxes. the study, which is fundamental to understanding vortex motion, is based largely on numerical integrations of the barotropic vorticity equation, using a finite‐difference method. In the absence of any large‐scale flow, the north‐westward drift of an initially symmetric, cyclonic vortex in the northern hemisphere is accompanied by a decrease in the tangential circulation at most radii, and a consequent deceleration of the azimuthally averaged tangential velocity. This behaviour is not simply a consequence of the increase in the Coriolis parameter over the domain of the cyclone as is often supposed, but may be explained as the sum of three effects: the outwards radial flux of relative vorticity associated with the asymmetric component of flow, the corresponding flux of planetary vorticity, and the rate of change in planetary vorticity due to the meridional displacement of the vortex. In particular, the net rate of change in absolute vorticity, the sum of the last two effects, makes the largest contribution to the circulation changes. the flux of absolute vorticity is associated, inter alia , with the generation of Rossby waves by the vortex. the behaviour is different from that in recent calculations by Carr and Williams in which the flux of planetary vorticity was omitted. It is pointed out that in the analytic theory for vortex motion developed by the first author and co‐workers, an initially symmetric vortex with zero net relative circulation at large radial distances subsequently develops a finite negative relative circulation whose strength increases linearly with time; this is because the net flux of planetary vorticity at large radial distances is finite. In contrast, in the numerical model the flux is close to zero so that the symmetric circulation decays more rapidly with radius than the 1/(radius) decay rate in the analytic model. At inner radii there is good qualitative agreement between the predictions of the two methods, even though there are quantitative differences between them. It is noted that the occurrence of the finite circulation in the analytic theory violates a theorem of Flierl et al. and that it represents a limitation of the long‐term validity of the theory.