An Asymptotic, Nonlinear Model for Anisotropic, Large-Scale Flows in the Tropics
S. Dolaptchiev (September 2005)
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.
