A PRELIMINARY STUDY ON THE INSTABILITY AND DEVELOPMENT OF THE ULTRA-LONG WAVES

This paper deals with the problem of the instability and development of the ultralong waves in frictionless and adiabatic motion.It is found that the controlling factors on the instability are the vertical distribution of the static stability and the vertical shear of the basic current.The occurrence of the instability requires that the upper layer of the atmosphere possesses higher static stability than the lower layer.The existence of the stratosphere provides this requirement.Further the degree of instability increases with the value of the shear.Taking the considerations of the feedback effect of the disturbances (ultra-long waves） on the basic field,equations concerning the variations of the static stability and the vertical shear of the basic westerlies are derived.From the condition that d/dt(P+K=0 the time required for the unstable disturbance to grow to its maximum intensity and the final amplitude (i.e.the maximum amplitude) are computed.P'and K'are respectively the eddy potential (including internal) energy and the kinetic energy per wave length.The theoritical findings agree with the observations.It is further found that the final maximum amplitude of an unstable ultra-long wave depends only on the structure of the initial state of the basic field,but not on the initial state of the disturbance.