Barotropic Vortex Stability to Perturbations from Axisymmetry

L. E. Carr III Department of Meteorology, Naval Postgraduate School, Monterey, California

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R. T. Williams Department of Meteorology, Naval Postgraduate School, Monterey, California

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Abstract

Tropical cyclones and dynamically similar model vortices robustly maintain a near-axisymmetric horizontal structure where the vortex flow is strongly nonlinear in spite of persistent asymmetric forcing represented by horizontal variations in the environmental winds and the Coriolis parameter. Since tropical cyclone motion relative to environmental “steering” has been associated with vortex asymmetries in even the simplest numerical models, identification of a barotropic mechanism that stabilizes vortices to dispersive influences is important.

A nondivergent, barotropic analytical model is used to identify the asymmetry-damping influence of symmetric angular windshear as the mechanism by which a barotropic vortex resists asymmetric forcing. Solutions are obtained for the evolution of linear asymmetric perturbations imposed as initial conditions on a steady, Rankine vortical flow. Perturbations combining various radial and azimuthal structures that might be expected from environmental and convective forcing are shown to damp with time in an algebraic “continuous spectrum” manner similar to perturbations imposed on f-plane barotropic Couette flow. Closed-form solutions to the model are used to explain why the damping rate is proportional to perturbation azimuthal wavenumber and the local magnitude of the symmetric angular windshear. The damping process is formally shown to be a barotropically stable energy transfer from perturbation to symmetric vortex, and independent numerical evidence is presented to verify the accuracy of the model. The energy transfer process is used to explain barotropic vortex adjustment to changes in external forcing, particularly the initial adjustment phase of a symmetric vortex in response to steady asymmetric forcing that has been documented in various numerical simulations of tropical cyclone motion.

Abstract

Tropical cyclones and dynamically similar model vortices robustly maintain a near-axisymmetric horizontal structure where the vortex flow is strongly nonlinear in spite of persistent asymmetric forcing represented by horizontal variations in the environmental winds and the Coriolis parameter. Since tropical cyclone motion relative to environmental “steering” has been associated with vortex asymmetries in even the simplest numerical models, identification of a barotropic mechanism that stabilizes vortices to dispersive influences is important.

A nondivergent, barotropic analytical model is used to identify the asymmetry-damping influence of symmetric angular windshear as the mechanism by which a barotropic vortex resists asymmetric forcing. Solutions are obtained for the evolution of linear asymmetric perturbations imposed as initial conditions on a steady, Rankine vortical flow. Perturbations combining various radial and azimuthal structures that might be expected from environmental and convective forcing are shown to damp with time in an algebraic “continuous spectrum” manner similar to perturbations imposed on f-plane barotropic Couette flow. Closed-form solutions to the model are used to explain why the damping rate is proportional to perturbation azimuthal wavenumber and the local magnitude of the symmetric angular windshear. The damping process is formally shown to be a barotropically stable energy transfer from perturbation to symmetric vortex, and independent numerical evidence is presented to verify the accuracy of the model. The energy transfer process is used to explain barotropic vortex adjustment to changes in external forcing, particularly the initial adjustment phase of a symmetric vortex in response to steady asymmetric forcing that has been documented in various numerical simulations of tropical cyclone motion.

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