On quasi-geostrophic, finite-amplitude disturbances forced by topography and diabatic heating

It is shown that, in the absence of dissipation, the tropographically-forced disturbances that Charney and Eliassen obtained as solutions to the linearized barotropic vorticity equation are actually finite-amplitude solutions. Similarly, in a baroclinic quasi-geostrophic model with no dissipation, topographically-forced disturbances obtained as solutions to the linearized potential vorticity equation are also shown to satisfy the non-linear version of the latter, and are therefore finite-amplitude solutions for arbitrary shapes of the topography, provided the mean zonal wind ū is such that the index of refraction is a function of the vertical coordinate only. Finally, it is shown that when ū satisfies the above condition, finite-amplitude thermally-forced disturbances of the kind discussed by Mitchell and Derome can coexist with the topographically-forced flow without interacting.