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An axisymmetric model of a mature tropical cyclone incorporating azimuthal vorticity
Author(s) -
Pearce Robert P.
Publication year - 2004
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 - 10.1256/qj.02.86
Subject(s) - vorticity , physics , mechanics , eye , vortex , radius , advection , circulation (fluid dynamics) , zonal and meridional , positive vorticity advection , thermal wind , potential vorticity , angular momentum , rotational symmetry , wind speed , classical mechanics , atmospheric sciences , meteorology , wind shear , tropical cyclone , thermodynamics , computer security , computer science
The inner core of an axisymmetric mature hurricane‐type vortex is first constructed using the gradient‐wind‐balance condition by specifying the tangential wind, v , and the mean temperature excess of the eye, which is assumed to be at rest. These parameters are used to define the configuration of the eye wall. A relation is then obtained relating the eye radius to a parameter α in the relation r α v =constant, defining the inflow tangential wind at radius r , a parameter Γ involving v (= v R ) at a radius R of order 100 km, and the eye temperature. This relation is shown to be readily adaptable to a model with an eye in solid rotation. A meridional circulation is constructed by specifying its azimuthal vorticity, η, and then calculating the temperature field required to maintain a steady state; the full azimuthal vorticity equation rather than the gradient‐wind‐balance approximation is used for this purpose. The main additional terms are those arising from vorticity advection by the meridional flow and a vorticity source related to the temperature lapse rate. The latter is the dominant additional term and implies model tangential winds which are about 5% supergradient near the eye wall. The role of the meridional circulation in both exporting the heat and importing the angular momentum required by the surface transfers is examined. The observed restriction of α to a narrow band between 0.5 and 0.6 is shown to be consistent with its being determined by the ratio given by the strength of the surface heating divided by the mean temperature excess in the eye. (=Δ T E), which must itself be restricted within a narrow band and can be regarded as determining α. It is inferred that the model's maximum wind is effectively determined solely by Δ T E. On the other hand, the eye radii of similar systems are roughly proportional to R , i.e. larger systems of similar intensities have larger eyes. Finally a conceptual model of the intensification phase is presented. After first demonstrating that a ring of deep convection must contract, it is shown that the intensification process can be characterized as a downwards and inwards penetration of the eye wall from the convective ring outflow near the tropopause, limiting the contraction. Copyright © 2004 Royal Meteorological Society