A numerical study of strongly nonlinear baroclinic instability

Inviscid and viscous stability analysis has been conducted numerically for the strongly nonlinear baroclinic flow in an annulus. An Eady model, modified by two Ekman layers of different strengths, is employed and by using a truncated spectral expansion, the model is reduced to a nonlinear automomous system of equations which describes the dynamics of several zonal wave number disturbances with its lower two meridional y-modes, and of the mean flow correction with its lowest four meridional y-modes. Each y-mode consists of a baroclinic and a barotropic pattern. Linear instability of the flow in the annulus is discussed for the stratification parameter S and dissipation δ. In the strongly unstable inviscid case, for different initial perturbation, the wave goes through an amplitude vacillation cycle for different time length, and finally, develops into irregular motion. In the viscous nonlinear analysis, axisymmetric flow, traveling steady waves and amplitude vacillation are found in the model. The difference between the solutions of several zonal wave number and that of single zonal wave number are checked. With S decreasing, i.e., radial temperature difference decreases if the rotation rate is fixed, the zonal wave number transition occurs, and this transition phenomena does not depend on the initial perturbation but is determined by the characteristics of the flow. The meridional mode number transition occurs while the supercriticality increases. The higher Ekman dissipation damps the flow faster than that of the lower one. The large dissipation damps the disturbance more effectively than the larger stratification does. The comparison of the present numerical results with experiments and existing analytical result shows good agreement.