The Role of Transient Motions in the Formation of Quasi-Stationary Planetary Waves

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  • 1 Department of Earth Sciences, Faculty of Education, Wakayama University, Wakayama, 640 Japan
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Abstract

We investigate numerically, using bifurcation theory, the formation of quasi-stationary planetary waves in the winter troposphere, i.e., of time-mean waves with large energy conversion from eddy available potential to eddy kinetic energy. The models used are quasi-geostrophic, two-level, highly truncated spectral ones, with topography of gradually increasing complexity. An external heating of newtonian type is given. The meridional difference of the radiative equilibrium temperatures (δT) is assumed to be the only variable parameter, all other external parameters taking constant, realistic values. How the nature of solutions changes with ΔT is examined.

The conclusions are as follows: The originally stationary solutions pass through two Hopf bifurcations when ΔT increases. Periodic solutions appear at the first Hopf bifurcation and, at the next bifurcation, chaotic solutions are generated. The quasi-stationary waves (the time-mean waves) in the chaotic state show properties distinct from truly stationary waves. That is, they are displaced eastward with respect to the stationary waves, the phase difference between the barotropic and baroclinic mode is large and the amplitude of the barotropic mode becomes relatively large. The energy conversion from eddy available potential energy to eddy kinetic energy is large, which coincides well with observations. Even if long waves are incorporated into the models, the aforestated properties of quasi-stationary waves still exist, although wave-wave interactions make them harder to see. Transient motions thus play essential roles in the formation of quasi-stationary planetary waves in the winter troposphere, even if Reynolds stress terms in time-mean equations are small.

Abstract

We investigate numerically, using bifurcation theory, the formation of quasi-stationary planetary waves in the winter troposphere, i.e., of time-mean waves with large energy conversion from eddy available potential to eddy kinetic energy. The models used are quasi-geostrophic, two-level, highly truncated spectral ones, with topography of gradually increasing complexity. An external heating of newtonian type is given. The meridional difference of the radiative equilibrium temperatures (δT) is assumed to be the only variable parameter, all other external parameters taking constant, realistic values. How the nature of solutions changes with ΔT is examined.

The conclusions are as follows: The originally stationary solutions pass through two Hopf bifurcations when ΔT increases. Periodic solutions appear at the first Hopf bifurcation and, at the next bifurcation, chaotic solutions are generated. The quasi-stationary waves (the time-mean waves) in the chaotic state show properties distinct from truly stationary waves. That is, they are displaced eastward with respect to the stationary waves, the phase difference between the barotropic and baroclinic mode is large and the amplitude of the barotropic mode becomes relatively large. The energy conversion from eddy available potential energy to eddy kinetic energy is large, which coincides well with observations. Even if long waves are incorporated into the models, the aforestated properties of quasi-stationary waves still exist, although wave-wave interactions make them harder to see. Transient motions thus play essential roles in the formation of quasi-stationary planetary waves in the winter troposphere, even if Reynolds stress terms in time-mean equations are small.

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