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THREE-DIMENSIONAL DISTURBANCES IN A BAROCLINIC ZONAL CURRENT

Hsiao-Lan KuoMassachusetts Institute of Technology

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Abstract

In the first part of this paper, the partial differential equations governing the three-dimensional large-scale disturbances in a baroclinic zonal current are derived by applying a semi-Lagrangian coordinate system. These equations are of second order and elliptic type, in not too low latitudes. Similar equations can also be obtained by assuming geostrophic approximations for the meridional velocity and the vorticity about the vertical, but this leads to the neglect of terms one order of magnitude smaller. The effect of viscosity is introduced by applying this approximation. A non-linear equation for the geostrophic wind-field is also obtained in the appendix.

In the second part, the disturbances in a basic current increasing linearly with height but independent of latitude are discussed, and the results show that most of the disturbances are unstable and that the amplitude of the most unstable disturbances may be doubled within 24 hours. The structure of these disturbances is rather similar to that observed in the atmosphere. These disturbances produce a downward transport of zonal momentum and a northward transport of heat, both of the same order of magnitude as are actually observed. It is also found that most of the perturbation kinetic-energy is produced by the horizontal pressure-force in the lower part of the atmosphere.

Abstract

In the first part of this paper, the partial differential equations governing the three-dimensional large-scale disturbances in a baroclinic zonal current are derived by applying a semi-Lagrangian coordinate system. These equations are of second order and elliptic type, in not too low latitudes. Similar equations can also be obtained by assuming geostrophic approximations for the meridional velocity and the vorticity about the vertical, but this leads to the neglect of terms one order of magnitude smaller. The effect of viscosity is introduced by applying this approximation. A non-linear equation for the geostrophic wind-field is also obtained in the appendix.

In the second part, the disturbances in a basic current increasing linearly with height but independent of latitude are discussed, and the results show that most of the disturbances are unstable and that the amplitude of the most unstable disturbances may be doubled within 24 hours. The structure of these disturbances is rather similar to that observed in the atmosphere. These disturbances produce a downward transport of zonal momentum and a northward transport of heat, both of the same order of magnitude as are actually observed. It is also found that most of the perturbation kinetic-energy is produced by the horizontal pressure-force in the lower part of the atmosphere.

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