Nonlinear equilibration of two-dimensional Eady waves

The initial-value problem for Eady's model is reexamined using a two-dimensional (x-z) primitive equation model. It is generally accepted that a finite amplitude instability of Eady's basic state will produce a frontal discontinuity in a finite time. When diffusion prevents the frontal discontinuity from forming, the wave amplitude eventually stops growing and begins to oscillate. We analyze this equilibration and suggest that it is a result of enhanced potential vorticity in the frontal region that is mixed into the interior from the boundaries. The dynamics of equilibration is crudely captured in a modified quasi-geostrophic model in which the zonal-mean static stability is allowed to vary. -from Authors