Nonlinear instability of a baroclinic flow

The stability for quasi-geostrophic disturbances of atmospheric currents is investigated for a continuously stratified model. The baroclinic disturbances in the atmosphere are initiated as the result of a hydrodynamic instability of the basic zonal current with respect to small perturbations of the flow. The perturbation equation with nonlinear boundary conditions is derived from the nonlinear theory of the quasi-geostrophic potential vorticity, and solved numerically by the pseudospectral method with the aid of the discrete Fourier transform and the fast transform. A numerical computer code is written and developed to obtain wave amplitudes for the spectrally expanded solution which are found from boundary conditions through time integrations by the Adams-Bashforth method.

The optimum time evolution of wave amplitudes depends upon the combination of three factors: grid points, physical plane size, and initial values. After the final time, 14 days, the blow-up in time integrations comes possibly from the instability condition of Eady linear model, atmospheric turbulence, and frontogenesis. Wave patterns show the principal picture of the nonlinear development of a linear wave. At the final time, the initially small perturbations produce a significant disturbance. So contours at the upper level exhibit atmospheric motions similar to cyclone or anti-cyclone, and wave surfaces at three different levels have the thermal wind-shear effect in the perturbed flow.