Wave–Mean Flow Statistics

Abstract

A relation between the statistics of large-scale waves and the mean flow is derived from the potential enstrophy equations integrated over an isobaric surface. The difference between time-averaged zonal-mean state and the radiative-dynamical equilibrium state due to the symmetric circulation is determined by three components: the steady wave enstrophy, the variance in the wave enstrophy and the variance mean flow enstrophy. With some simplifications, the relationship between these components can be used to estimate the maximum amplitude for Rossby waves derived from a statistical data set. We obtain an upper limit of ?1200 gpm for a wave disturbance with a meridional scale of ?1800 km. If the Rossby wave amplitudes are observed near that upper limit, then the wave energy spectrum should exhibit a ?5 power law. The three enstrophy components are estimated for a parameterized model of wave?mean flow interaction at a single level. We find that the steady wave enstrophy, the wave enstrophy variance and the mean enstrophy variance all are within a factor of 2 of each other with the wave variance being the largest. These results suggest that attempts to model the time-mean stratospheric structure in winter, using only the time-mean stationary wave forcing of the mean flow, may not be successful.