NUMERICAL-METHODS OF ESTIMATING BOUNDS ON THE NONLINEAR SATURATION OFBAROTROPIC INSTABILITY

Two numerical methods are presented for calculating rigorous upper bou nds on the finite-amplitude growth of barotropic instabilities to zona l jets on a rotating sphere. One of the methods is based on Shepherd ( 1988)'s analytic method, which uses the conservation law of domain-ave raged pseudomomentum density. A variational minimization problem is so lved numerically with a quasi-Newton method after discretization. The other is the authors' original method to solve a minimization problem under the constraints of the conservation laws of all Casimir invarian ts and total absolute angular momentum. The convex simplex method, whi ch has been used in operations research, is applied to solve a quadrat ic programming problem. The two methods are applied to estimate the up per bounds for several profiles of the initial unstable jet and the bo unds are compared with the results of non-linear time integrations fro m the unstable jet with a high-resolution model (Ishioka and Yoden, 19 94). The two bounds are found to be almost completely identical to eac h other. Evidence from high-resolution numerical experiments is that t he bounds overestimate the actual wave-enstrophy achieved in numerical experiments by a factor of 1.2 to 2.3.