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Tropical Cyclone Size Is Strongly Limited by the Rhines Scale: Experiments with a Barotropic Model

Kuan-Yu LuaDepartment of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, Indiana

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Daniel R. ChavasaDepartment of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, Indiana

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Abstract

Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradient β. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect of β varies with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on a β plane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradient β and initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex to β. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is well described by the vortex Rhines time scale, which is defined as the overturning time scale of the circulation at the vortex Rhines scale and is shown to be directly related to the Rossby wave group velocity. The relationship between our idealized results and the real Earth is discussed. Results may generalize to other eddy circulations, such as the extratropical cyclone.

Significance Statement

Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kuan-Yu Lu, lu711@purdue.edu

Abstract

Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradient β. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect of β varies with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on a β plane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradient β and initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex to β. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is well described by the vortex Rhines time scale, which is defined as the overturning time scale of the circulation at the vortex Rhines scale and is shown to be directly related to the Rossby wave group velocity. The relationship between our idealized results and the real Earth is discussed. Results may generalize to other eddy circulations, such as the extratropical cyclone.

Significance Statement

Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kuan-Yu Lu, lu711@purdue.edu
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