Numerical Solution of a 2-D Model for the Formation of Zonal Jets

The generation and slow evolution of zonal jets in a 2-D flow with beta effect is examined using the model developed by Manfroi and Young. The original model was derived by the perturbation method from the barotropic vorticity equation with a sinusoidal meridional mean flow. The leading order equation is 2-D. Nevertheless, Manfroi and Young focused on solving a slightly reduced 1-D version of the equation which already produces rich dynamics of zonal jets. This study attempts at some numerical solutions of the 2-D version of Manfroi-Young model which includes a term, controlled by the parameter β₀, that represents the effect of large-scale Rossby waves. The system is entirely deterministic and is integrated forward in time by a standard finite-difference scheme without any additional forcing. Numerical solutions are explored in the parameter space spanned by (β₀, μ) where μ is the coefficient of bottom drag. The results indicate that the behavior of zonel jets in the 2-D case is qualitatively similar to that in the reduced 1-D case. When μ = 0, the jets continue to merge in time. Steady jets form under a non-zero bottom drag. The 2-D simulations affirm the critical boundary that demarcates formation and absence of jets as originally analyzed by Manfroi and Young. The detailed dependence of the scale and intensity of the jets on the (β₀, μ) parameters will be discussed.