A mixed spectral and finite difference model to study baroclinic annulus waves

A mixed spectral and finite difference model to study finite amplitude baroclinic waves in a differentially heated rotating annulus is presented. The model consists of the full Navier-Stokes equations and the heat equation. The field variables f = f(r, φ z; t) are decomposed into zonally averaged components f_o(r, z; t) and eddy components f(r, φ, z; t), the latter being periodic in f and represented in terms of Fourier series. The unknowns f_o(r, z; t) and f^{c, s}(r, z; t), which are Fourier amplitudes of f′(r, φ, z; t) are governed by two-dimensional primitive equations with the addition of source terms. These equations are solved semi-implicitly by the alternating direction implicit method on variable grids.A simplified model with two Fourier components which permits self-interaction of the chosen wave and the interaction of the wave and the mean fields had been used to repeat a computation done by G. P. Williams, who used a fully three-dimensional finite difference algorithm. We can reproduce almost all of Williams' results in 1/20 of the computing time with the present model. It only requires 1/30 the additional computer storage of Williams' finite difference model over the axisymmetric problem.The potential of the present model for investigation of multiwave interaction as well as the advantages and disadvantages of the two different approaches is discussed.