East Asia and Western Pacific METEOROLOGY AND CLIMATE

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where b=g(T-Tr)/Tr buoyance force, N=g (^J -V") /Tr the
squared buoyance frequency, is gee-potential height, f is
the Coriolis force, T and 0 are temperature and potential
temperature in cloud, respectively, Tr and 6t* are the
environmental temperature and potential temperature,
respectively, y- the temperature lapse rate, and Yd tne ^
adiabatic lapse rate. Also, ^*fcj, (v*--l/r* }u+k z^^^ ^ A^Uk
~!4*)ir+fec^«X«o , AOM^c^/r*>^^^
and H is the scale height, i.e., H=RT 0 /g. Other symbols are
conventional ones.
Averaging the equation set (1) over an approriate
area,- one may obtain those terms which respresent the
effects of culumus convection. Then, in order to transform
the resulting set of equations into dimensionless form, one
may introduce the following variables;
-t* ,
absolut vorticity
inertial parameter'
vertical shear 1%
Fronde number F r ss
aspect ratio A*.=s -
quantities.
* J «
5^* ,. Rossby number
/• Richardson number Rj
» "*" denotes dimensionless
We further expand each variable in terms of a small
parameter d.=U/v. After some mathematical manipulation, we
can derive a diagnostic equation of the secondary
circulation for the tropical cyclone:
where Vis the stream function,
and "VJ5*« /k*j^* d 54|^" While introducing the above streamfunction,,
the isothermal atmosphere with the temperature T
is assumed. In this case, the height Z defined with z--
Hlnp/p is just eqxaal to the actual height,
The elliptic condition for the equation (2) is D
--CS"^>*>O.The observed data were used to estimate D* and we
find that all the grid points of the domain under study
satisfy the elliptic condition of Er>0.