Conditional Nonlinear Optimal Perturbations Of A Two-Dimensional Quasigeostrophic Model With β Effect

In this thesis, we use a derivative-free optimization method with penalty function to compare conditional nonlinear optimal perturbations(CNOPs) of a two-dimensional quasi-geostrophic model with linear optimal perturbations under the solid wall bound-ary condition. The advantages of this approach are that the scheme of adjoint model is not required and the workload is reduced. The numerical experiment results demon-strate that: if the constraint is enough small, the tangent linear model(TLM) can be well used to approximate the nonlinear model(NLM), and conditional nonlinear op-timal perturbations are the same as the linear optimal perturbations; if the constraint is large, the tangent linear model can not be used to approximate the nonlinear model due to the effect of nonlinearity, and conditional nonlinear optimal perturbations are different from the linear optimal perturbations;β effect has a very strong stability, moreover, as β becomes large, the stability will become strong.