Generalized Nonlinear Subcritical Symmetric Instability

Starting from nonlinear equations on the f-plane containing frictional dissipation under the Boussinesqapproximation, a new kind of generalized energy is proposed as the Lyapunov function, and averages aretaken as any functions of (x, z) instead of the commonly-used means of bilinear functions of (x, z), therebyresulting in a new criterion of generalized nonlinear symmetric stability. It shows that not only mustthe dissipative coefficient be greater than a certain critical value but the initial disturbance amplitudemust be synchronously smaller than another marginal value as well. It follows that the latter imposesa crucial constraint on the former, thus leading to the fact that when the amplitude is bigger comparedto another critical value, generalized nonlinear subcritical symmetrical instability 05- occur. The newcriterion contributes greatly to the improvement of the previous results of its kind.