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Noise-Induced Interhemispheric Particle Transport—Stochastic Resonance in a Hamiltonian System

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  • 1 Department of Atmospheric Sciences, Institute of the Earth Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract

A Lagrangian model is employed to study the characteristics of a horizontal cross-equatorial flow. The Coriolis force and the mean meridional pressure field assumed here render the dynamics of particle flow across the equator a nonlinear Hamiltonian system of a bistable potential that has a local maximum at the equator. In the absence of any additional forces this local maximum at the equator prohibits particles from flowing from one hemisphere to the other. When all other (i.e., in addition to the mean meridional pressure gradient) forces are introduced into the system as stochastic forcing, modeled by Gaussian white noise, anomalous diffusion up the mean pressure gradient occurs and particles launched in one hemisphere can reach the other. Spectral estimations of equator crossing events show that at low noise intensity the spectral peak is low, narrow, and situated at low frequencies, and that as the amplitude of the noise increases, the peak becomes higher, wider, and shifts toward higher frequencies. At very large noise intensities the spectral peak flattens out, which implies that the process of equator crossing becomes noise dominated. The results demonstrate the existence of an optimal noise intensity where the signal-to-noise ratio of equator crossings exhibits a sharp maximum, and this optimal noise intensity is insensitive to the precise value of the mean meridional pressure gradient. These findings are applicable to the terrestrial atmosphere where the mean meridional geopotential height gradient and the (zonal and temporal) deviations from it are of the same order.

These results demonstrate, for the first time, the occurrence of stochastic resonance in a Hamiltonian system.

Corresponding author address: Dr. Nathan Paldor, Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem, 91904, Isreal.

Email: dvorkin@vms.huji.ac.il; paldor@vms.huji.ac.il

Abstract

A Lagrangian model is employed to study the characteristics of a horizontal cross-equatorial flow. The Coriolis force and the mean meridional pressure field assumed here render the dynamics of particle flow across the equator a nonlinear Hamiltonian system of a bistable potential that has a local maximum at the equator. In the absence of any additional forces this local maximum at the equator prohibits particles from flowing from one hemisphere to the other. When all other (i.e., in addition to the mean meridional pressure gradient) forces are introduced into the system as stochastic forcing, modeled by Gaussian white noise, anomalous diffusion up the mean pressure gradient occurs and particles launched in one hemisphere can reach the other. Spectral estimations of equator crossing events show that at low noise intensity the spectral peak is low, narrow, and situated at low frequencies, and that as the amplitude of the noise increases, the peak becomes higher, wider, and shifts toward higher frequencies. At very large noise intensities the spectral peak flattens out, which implies that the process of equator crossing becomes noise dominated. The results demonstrate the existence of an optimal noise intensity where the signal-to-noise ratio of equator crossings exhibits a sharp maximum, and this optimal noise intensity is insensitive to the precise value of the mean meridional pressure gradient. These findings are applicable to the terrestrial atmosphere where the mean meridional geopotential height gradient and the (zonal and temporal) deviations from it are of the same order.

These results demonstrate, for the first time, the occurrence of stochastic resonance in a Hamiltonian system.

Corresponding author address: Dr. Nathan Paldor, Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem, 91904, Isreal.

Email: dvorkin@vms.huji.ac.il; paldor@vms.huji.ac.il

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