Topographic Waves in Nonlinear and Linear Spherical Baratropic Models

Abstract

The effects of topography in forcing the stationary eddy flow field of the atmosphere have been examined using the spherical equivalent barotropic model. Fully nonlinear solutions obtained using the methods of equilibrium statistical mechanics have been compared and contrasted with linearized steady-state solutions, and both of these have been compared with observed flows. Incorporation of nonlinear effects eliminates the resonant behavior characteristic of the linear solutions and thus leads to wide differences between the two types of solutions. Whereas the linear solutions are strongly dependent on the strength of the zonal flow, the qualitative appearance of the nonlinear eddy fields is remarkably constant over a wide variation of the relevant parameters and is essentially a filtered version of the topographic field. The nonlinear fields also show no evidence of the wavetrains which are such a striking feature of the linear fields. Comparison with observed fields shows nonlinear effects to be most important at low altitudes. The nonlinear stationary flow field at 850 mb gives as realistic a representation of the qualitative observed features as can be produced by much more complicated models, whereas the linear field shows far too much structure. At high levels, where the zonal flow is stronger, the linear approximation (including drag) is better than at low levels.