Sardeshmukh, P., C. Penland, and M. Newman, 2001: Rossby waves in a fluctuating medium. In Stochastic Climate Models, P. Imkeller and J.-S . von Storch (Eds.), Progress in Probability, 49, Birkhauser-Verlag, 369-384.
It is well known that rapid fluctuations of the zonal mean wind speed can contribute significantly to the variability of planetary-scale atmospheric waves (Rossby waves). What seems to be less appreciated is that these same fluctuations can also contribute to the climatological mean wave pattern. In this study, the extent to which stochastic zonal wind fluctuations affect the mean and variance of the wave response to steady forcing is investigated in the context of a simple numerical model of the global atmosphere, i.e. a barotropic vorticity equation model. It is first shown that rapid variations of the zonal wind can justifiably be treated as stochastic. Then, the appropriate modifications to the barotropic vorticity equation are derived using the classical theory of stochastic differential equations. Finally, the effect of the stochastic fluctuations on the mean Rossby-wave response is illustrated in two qualitatively different cases. The first experiment considers stochastic fluctuations in the zonally-symmetric component of the wind, and it is shown that those fluctuations amount to a net damping of the Rossby wave. In the second experiment, random fluctuations in the frictional damping are considered, and are shown to have a net destabilizing influence.