THE LYAPUNOV STABILITY OF NONLINEAR WAVE MOTION IN THE BAROTROPIC NONDIVERGENT ATMOSPHERE

Introducing the concept of pseudo-momentum, a generalized Arnold-Dikii functional is established, and then the sufficient condition for stability of nonlinear wave motion in the barotropic nondivergent atmosphere is derived by use of variational principle. It is found that the stability of nonlinear wave motion depends not only on its streamfield distribution, but also on its phase speed for the propagating nonlinear wave motion. Moreover, the stability criterion of travelling modon is also obtained, and it is shown that the travelling modon is stable if the scale of disturbance superimposed on the travelling modon remains to be less than that of the travelling modon.