Title:

An Analysis of a Mature Hurricane Using a Mathematical Model

This study is concerned with the dynamic and thermodynamic
structure of hurricane type circulations. The storm is taken
to be symmetric about a vertical axis through its centre, and
cylindrical isobaric polar coordinates are used throughout.
The possibility of obtaining a time dependent solution by the
use of time similarity variables is explored.
An analytic solution is found for the dynamical equations
of a mature hurricane system in a quasistationary state. The
solution is based on (i) eddy viscosity coefficients Kl and
K2, describing vertical and horizontal transfers of momentum
respectively, expressed initially as general functions of p ,
and (ii) the premise that the radial variation in the
magnitudes of the tangential and radial components of velocity
are of a similar form. Explicit expressions for Kl and K2
are finally obtained by choosing power law forms, in the p
variable, which lead to good agreement between model results
and typical observed distributions of the three mean velocity
components over the dynamically active region of the storm.
By using this (inverse) method of calculating Kl and K2
and an analytic model, the whole eddy system, ranging from
those created by the very strong velocity shear close to the
sea surface to those connected with violent cloud convection,
is described by continuous mathematical functions. The need
for a separate boundary layer is avoided. The associated
temperature and condensation heating distributions are then
calculated from the hydrostatic relation and the thermodynamic
equation. To complete the model an integral flux condition
for the total evaporation from the sea surface is used to
obtain the sea surface temperature for a given input of
water vapour at the outer wall of the model.
Numerical experiments are carried out which, together
with an examination of the basic functional forms involved
in the solution, enable the model dynamics to be related to
changes in the numerical values of various physical parameters.
By considering the model sea temperature for storms having a
given kinetic energy, the preferred radial distribution of
tangential velocity for such a storm is obtained. It is found
that the height of the maximum tangential velocity, the
'steering height', is required to be between 850 and 900mb
from thermal considerations. The range of functional variation
in the formulation of the eddy terms that can support realistic
storm cells is examined, and an investigation is made of the
consequences of variation in the Coriolis parameter.
