An Analytical Theory of Tropical Cyclone Motion Using a Barotropic Model

Smith, Roger K.; Ulrich, Wolfgang

doi:10.1175/1520-0469(1990)047<1973:aatotc>2.0.co;2

Cited by 47 publications

(26 citation statements)

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“…(d) The β-drift: the reader might be missing an explicit representation of the beta-drift (see e.g. Smith & Ulrich 1990;Smith 1991;Reznik 1992;Reznik & Kizner 2007b) in (5.17), which is the technical term for the self-induced motion of a vortex due to the large-scale transport of the horizontally inhomogeneous planetary rotation. According to Reznik & Kizner (2007b) the order of magnitude of the β-drift velocity is U β ∼ βL 2 syn , where L syn is the Rossby deformation radius.…”

Section: Limitations Of the Present Theory And Outlookmentioning

confidence: 99%

“…Asymptotic theories that resolve the vortex core structure and describe its coupling to the environmental flow and/or the motion of its centre were developed by Ling & Ting (1988) in the limit of geostrophic balance, by Smith & Ulrich (1990) and Smith (1991) for two-dimensional flow on a β-plane, and by Reznik & Grimshaw (2001) and McWilliams, Graves & Montgomery (2003) in the context of shallow-water theory. By restricting to two-dimensional shallow-fluid models, these theories cannot address the vertical structure of the flow and, especially, a possible tilt of the vortex axis.…”

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confidence: 99%

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Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

Päschke

Marschalik

Owinoh³

et al. 2012

J. Fluid Mech.

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A strongly tilted, nearly axisymmetric vortex in dry air with asymmetric diabatic heating is analysed here by matched asymptotic expansions. The vortex is in gradient wind balance, with vortex Rossby numbers of order unity, and embedded in a quasigeostrophic (QG) background wind with weak vertical shear. With wind speeds of 60-120 km h −1, such vortices correspond to tropical storms or nascent hurricanes according to the Saffir-Simpson scale. For asymmetric heating, nonlinear coupling of the evolution equations for the vortex tilt, its core structure, and its influence on the QG background is found. The theory compares well with the established linear theory of precessing quasi-modes of atmospheric vortices, and it corroborates the relationship between vortex tilt and asymmetric potential temperature and vertical velocity patterns as found by Jones (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 821-851) and Frank & Ritchie (Mon. Weath. Rev., vol. 127, 1999, pp. 2044-2061 in simulations of adiabatic tropical cyclones. A relation between the present theory and the local induction approximation for three-dimensional slender vortex filaments is established.

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Section: Limitations Of the Present Theory And Outlookmentioning

confidence: 99%

mentioning

confidence: 99%

Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

Päschke

Marschalik

Owinoh³

et al. 2012

J. Fluid Mech.

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“…However, since the initial vortex possesses a monotonic PV distribution, a related vortex-segregation mechanism is available. From vortex-motion theory (McWilliams and Flierl, 1979;Smith and Ulrich, 1990;Schecter and Dubin, 1999), intense cyclonic vorticity anomalies generally move 'up the ambient vorticity gradient', and vice versa for anticyclonic vorticity anomalies. Therefore intense cyclonic anomalies immersed in the negative vorticity gradient of the parent vortex will tend to move toward the centre, and anticyclonic anomalies will tend to move away from the centre.…”

Section: Relative-vorticity Structurementioning

confidence: 99%

“…Fiorino and Elsberry, 1989;Smith and Ulrich, 1990;Smith and Weber, 1993), we consider the horizontal vorticity asymmetries of the ensemble experiments B0-B10 on all three domains. A combined multiple-grid configuration of domains 1 (45 km grid size) and 2 (15 km grid size) is set up as follows.…”

Section: Experiments On a β-Planementioning

confidence: 99%

Tropical‐cyclone intensification and predictability in three dimensions

Sáng¹,

Smith²,

Montgomery

2008

Quart J Royal Meteoro Soc

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241

105

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ABSTRACT:We present numerical-model experiments to investigate the dynamics of tropical-cyclone amplification and its predictability in three dimensions. For the prototype amplification problem beginning with a weak-tropical-storm-strength vortex, the emergent flow becomes highly asymmetric and dominated by deep convective vortex structures, even though the problem as posed is essentially axisymmetric. The asymmetries that develop are highly sensitive to the boundarylayer moisture distribution. When a small random moisture perturbation is added in the boundary layer at the initial time, the pattern of evolution of the flow asymmetries is changed dramatically, and a non-negligible spread in the local and azimuthally-averaged intensity results. We conclude, first, that the flow on the convective scales exhibits a degree of randomness, and only those asymmetric features that survive in an ensemble average of many realizations can be regarded as robust; and secondly, that there is an intrinsic uncertainty in the prediction of maximum intensity using either maximumwind or minimum-surface-pressure metrics. There are clear implications for the possibility of deterministic forecasts of the mesoscale structure of tropical cyclones, which may have a major impact on the intensity and on rapid intensity changes.Some other aspects of vortex structure are addressed also, including vortex-size parameters, and sensitivity to the inclusion of different physical processes or higher spatial resolution. We investigate also the analogous problem on a β-plane, a prototype problem for tropical-cyclone motion. A new perspective on the putative role of the wind-evaporation feedback process for tropical-cyclone intensification is offered also.The results provide new insight into the fluid dynamics of the intensification process in three dimensions, and at the same time suggest limitations of deterministic prediction for the mesoscale structure. Larger-scale characteristics, such as the radius of gale-force winds and β-gyres, are found to be less variable than their mesoscale counterparts.

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“…On a 3-plane, however, as was shown by many theoretical and numerical studies (e. g., Chan and Williams, 1987;Willoughby, 1988;Fiorio and Elsberry, 1989;Smith and Ulrich, 1990;Li and Wang, 1994), the advection of the planetary vorticity by a symmetric cyclonic circulation generates asymmetries in the cyclone motion. The asymmetries are dominated by an azimuthal wave-numberone component.…”

Section: Introductionmentioning

confidence: 92%

An Equation of the β-Gyre Rotation of a Cyclone in a Non-uniformly Straining Environmental Flow

Kanehisa¹

1996

Journal of the Meteorological Society of Japan

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An Analytical Theory of Tropical Cyclone Motion Using a Barotropic Model

Cited by 47 publications

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Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

Tropical‐cyclone intensification and predictability in three dimensions

An Equation of the β-Gyre Rotation of a Cyclone in a Non-uniformly Straining Environmental Flow

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An Analytical Theory of Tropical Cyclone Motion Using a Barotropic Model

Cited by 47 publications

References 0 publications

Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

Motion and structure of atmospheric mesoscale baroclinic vortices: dry air and weak environmental shear

Tropical‐cyclone intensification and predictability in three dimensions

An Equation of the &beta;-Gyre Rotation of a Cyclone in a Non-uniformly Straining Environmental Flow

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An Equation of the β-Gyre Rotation of a Cyclone in a Non-uniformly Straining Environmental Flow