Nonlinear Circulations in a Symmetrically Unstable Flow

Qin Xu Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, OK 73019

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Abstract

The time solution of a transverse inviscid circulation in a basic flow possessing either symmetric instability (SI) or conditional symmetric instability (CSI) is studied. By making the assumption that the circulation pattern is arbitrary but invariable with times, it can be proven that (i) the time evolution of a SI circulation integral is periodic and similar to that of a large amplitude pendulum started from the unstable equilibrium position, (ii) the same feature exists for a CSI circulation integral only when the mass center of the circulation loop is just at the mean (latent) heating level, (iii) a CSI circulation will spin up like a forced large amplitude pendulum (or oscillate like a damping pendulum) if its mass center is above (or below) the mean heating level.

Abstract

The time solution of a transverse inviscid circulation in a basic flow possessing either symmetric instability (SI) or conditional symmetric instability (CSI) is studied. By making the assumption that the circulation pattern is arbitrary but invariable with times, it can be proven that (i) the time evolution of a SI circulation integral is periodic and similar to that of a large amplitude pendulum started from the unstable equilibrium position, (ii) the same feature exists for a CSI circulation integral only when the mass center of the circulation loop is just at the mean (latent) heating level, (iii) a CSI circulation will spin up like a forced large amplitude pendulum (or oscillate like a damping pendulum) if its mass center is above (or below) the mean heating level.

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