East Asia and Western Pacific METEOROLOGY AND CLIMATE

494
THE NONLINEAR INTERACTION OF INTERNAL
AND TURBULENCE
WAVE
Liu Shi-da
Department of Geophysics, Peking University
Beijing, China
ABSTRACT
We analyse the behaviour of nonlinear dynamical
systems in the form of Galerkin of turbulence equations.
These equations are presented by the models of Burger's
and Chao Jiping.
On the parameter plane (R-j»*O» "t^e
region is
divided into five different behaviour by bifurcation
point curves and limit point curves* They are mean
field 0, periodic internal-gravity wave P, convection
motion T, pulse wave S and turbulence behaviour C.
It is shown that these behaviour can transform into
one another through pitchfork bifurcation and Hope
bifurcation. Clearly, our result is better than that of
linear Miles theorem. In the case of stratified
stability, turbulence can also occur. If the initial
Richardson number R.is slightly larger than 0.25 and the
internal-gravity wave propagates through such a system
in which mean velocity is decreased and mean temperature
lapse rate is increased, then the new Richardson number
R.may become smaller than 0.25 and turbulence may occur.
This is also the reason that intermittency occurs
between the turbulence and internal-gravity wave. The