is the horizontally averaged wind vector over a cylindrical portion of the Doppler analysis domain (A = Rmax²) centered on the sto rm,

Rmax is defined as the largest radius that surrounds the center within the Doppler analysis domain at every level in the vertical. The vector is the deviation from

Taking advantage of the circular symmetry of the horizontal-storm wind field, we may in turn decompose V' into two components,

where is the symmetric component of the hurricane vortex, given by

and is the deviation from

In terms of a Fourier decomposition, corresponds to the wave number zero component of V. The vector V* is the remainder of the perturbation wind; i.e., that part not accounted for by the symmetric vorte x (wave numbers 1 and higher).

Equation (1) can now be written as