A Geometric Model of the Nonlinear Equilibration of Two-Dimensional Eady Waves

Abstract The initial-value problem for Eady's model is reexamined using a two-dimensional (x, z) Lagrangian semigeostrophic model. A basic-flow state in a periodic domain with a perturbation field imposed is represented by piecewise constant data. The Lagrangian conservation laws governing the motion allow the construction of a solution that describes the evolution of the unstable wave as it passes through the point of frontal collapse, reaches a maximum amplitude, and then decays. The integration is continued and a second cycle is observed. A similar experiment was performed by Nakamura and Held, using a primitive equation model with diffusion. Two integrations are carried out to investigate the sensitivity of the solution to the representation of the data by piecewise constant values and present observations and comparisons between these results and those of Nakamura and Held.