The Nonlinear Evolution of Disturbances to a Parabolic Jet

Abstract

Abstract It has been shown that the linearized equations for disturbances to a parabolic jet on a β plane, with curvature Un0(y) such that the basic-state absolute vorticity gradient β − Un0(y) is zero, ultimately become inconsistent in the neighborhood of the jet axis and that nonlinear effects become important. Numerical solutions of the nonlinear long-time asymptotic form of the equations are presented. The numerical results show that the algebraic decay of the disturbances as t−1/2 predicted by the linear equations is inhibited by the nonlinear formation of coherent vortices new the jet axis. These lead to a disturbance amplitude that decays only through the action of weak numerical diffusion but is otherwise as t0. The linear theory is extended to the case when the basic-state absolute vorticity gradient is nonzero but weak. When the gradient is weak and negative the decay is modified and is ultimately as t−3/2. When the gradient is weak and positive, on the other hand, a discrete eigenmode is excite...