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Zusammenfassung:
In order to investigate the atmospheric dynamics in the tropics, we applied an unified multiple scales asymptotic approach and derived reduced model equations. This technique combines methods from the multi-scale perturbation theory and the scale analysis in the theoretical meteorology. It can be used for multiple scales interaction studies. The systematic approach was applied to the 3D compressible equations for a fluid on an equatorial b-plane. An anisotropic asymptotic scaling was used, allowing to address flows on a sub-planetary length scale in zonal direction and on a mesoscale in meridional direction.
The reduced model equations consist of the WTG approximation and a nondivergent constraint on the flow in the y, z-plane. The momentum equation is time independent and have important nonlinear transport terms. The system of equations describes a model of a Hadley type circulation modified by a zonal pressure gradient force. After considering the magnitude of the different diabatic processes, we showed that convective heating will drive the circulation.
We have prescribed the potential temperature source term and analytical solutions for the meridional and vertical velocities were found. They describe ascending motions in the region of heating and descending in the region of cooling, a poleward flow in the upper and an equatorward flow in the lower atmosphere. To find solutions for the zonal wind, we considered the zonally averaged version of the x-component of the momentum equation. In the inviscid case we showed that the absolute zonal momentum per unit mass remains constant along stream lines. Numerical simulations were performed with a vertical diffusion representation of the turbulent momentum transport. The model predicts weak easterly surface winds and strong upper level westerlies at the boundary, corresponding to the subtropical jet at the edge of the Hadley cell. The meridional profile of the potential temperature is consistent with the geostrophic and hydrostatic balance in the model atmosphere. We have found that the momentum advection terms are large near the equator, especially in the region of heating.
