East Asia and Western Pacific METEOROLOGY AND CLIMATE

496
Burgers(l948) had put forward a simple turbulence
model [3 J . Chao(l962) extended Burgers model to include
temperature advection. The basic equations of the
Burger s-Chao model are as follows:
-a
„,
where U(t) and T(t) are horizontal velocity and
temperature averaged for height respectively, w(z,t) and
0(z,t) are perturb ational vertical velocity and
temperature respectively, P and Q are pressure gradient
force and heat source respectively, both of which are
necessary for the maintenance of initial mean motion UQ
and mean temperature T Q . The terms involving 3>
represent viscous dissipation. Eqs. (1)~(4) represent
the nonlinear dynamical system. The first terms on the
right hand of Eqs* (2) and (4) represent the mean field
acting on the perturbation fields. The third terms on
the right hand of Eqs. (1) and (3) represent the
perturbation field acting on the mean fields. £0 denotes
buoyancy force. 1iT^ and ^tfl^c
are advection terms.
^-.JL ^ ig ^g^ temperature, taken as a constant), j^
is the adiabatic lapse rate and H is the vertical
thickness.
The advection terms are omitted in Chao's model. The
temperature advection term ^M is included in our
model. Let