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  1. Abstract

    An idealized, three‐dimensional, 1 km horizontal grid spacing numerical simulation of a rapidly intensifying tropical cyclone is used to extend basic knowledge on the role of mean and eddy momentum transfer on the dynamics of the intensification process. Examination of terms in the tangential and radial velocity tendency equations provides an improved quantitative understanding of the dynamics of the spin‐up process within the inner‐core boundary layer and eyewall regions of the system‐scale vortex. Unbalanced and non‐axisymmetric processes are prominent features of the rapid spin‐up process. In particular, the wind asymmetries, associated in part with the asymmetric deep convection, make a substantive contribution (30%) to the maximum wind speed inside the radius of this maximum. The analysis provides a novel explanation for inflow jets sandwiching the upper‐tropospheric outflow layer which are frequently found in numerical model simulations. In addition, it provides an opportunity to assess the applicability of generalized Ekman balance during rapid vortex spin‐up. The maximum tangential wind occurs within and near the top of the frictional inflow layer and as much as 10 km inside the maximum gradient wind. Spin‐up in the friction layer is accompanied by supergradient winds that exceed the gradient wind by up to 20%. Overall, the results affirm prior work pointing to significant limitations of a purely axisymmetric balance description, for example, gradient balance/Ekman balance, when applied to a rapidly intensifying tropical cyclone.

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  2. Abstract

    Tropical cyclone formation and evolution at, or near, the Equator is explored using idealized three‐dimensional model simulations, starting from a prescribed, initial, weak counterclockwise rotating vortex in an otherwise quiescent,nonrotatingenvironment. Three simulations are carried out in which the maximum tangential wind speed (5 m s) is specified at an initial radius of 50, 100, or 150 km. After a period of gestation lasting between 30 and 60 hr, the vortices intensify rapidly, the evolution being similar to that for vortices away from the Equator. In particular, the larger the initial vortex size, the longer the gestation period, the larger the maximum intensity attained, and the longer the vortex lifetime. Beyond a few days, the vortices decay as the cyclonic vorticity source provided by the initial vortex is depleted and negative vorticity surrounding the vortex core is drawn inwards by the convectively driven overturning circulation. In these negative vorticity regions, the flow is inertially/centrifugally unstable. The vortex evolution during the mature and decay phases differs from that in simulations away from the Equator, where inertially unstable regions are much more limited in area. Vortex decay in the simulations appears to be related intimately to the development of inertial instability, which is accompanied by an outward‐propagating band of deep convection. The degree to which this band of deep convection is realistic is unknown.

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  3. Many previous diagnoses of the global kinetic energy budget for a tropical cyclone have given prominence to the global integral of a pressure–work term in the generation of kinetic energy. However, in his erudite textbookAtmosphere–Ocean Dynamics, Adrian Gill derives a form of the kinetic energy equation in which there is no such explicit source term. In this article we revisit the interpretations of the generation of kinetic energy given previously in light of Gill's analysis and compare the various interpretations, which are non‐unique. Further, although global energetics provide a constraint on the flow evolution, in the context of the kinetic energy equation they conceal important aspects of energy generation and consumption, a finding which highlights the limitations of a global kinetic energy budget in revealing the underlying dynamics of tropical cyclones.

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