Kurihara, Y., 1976: On the development of spiral bands in a tropical cyclone. Journal of the Atmospheric Sciences, 33 (6), 940-958.

Abstract: Development of the band structure in a tropical cyclone is investigated by solving an eigenvalue problem for perturbations of spiral shape. The perturbations are superposed on a baroclinic circular vortex accompanied with a radial and vertical basic flow.
It is shown that the spiral bands in three different modes may be intensified in an inner area of a tropical cyclone. The baroclinicity of a basic field is not required for the development of bands in any mode. A spiral band which propagates outward can grow in the presence of the horizontal shear of the basic azimuthal flow. Without the basic circular vortex, this band is reduced to a neutral gravity-inertia wave with a particular vertical structure. The unstable spiral in this mode takes a pattern which extends clockwise from the center of a storm in the Northern Hemisphere. An azimuthal wavenumber 2 and a radial scale (twice the band width) of 200 km are preferred by this band. Another band with the characteristics of an inward propagating gravity wave may be excited in an inner area of a storm by its strong response to the effect of diabatic heating. The third kind of band has the features of a geostrophic mode and moves inward. Its development in an inner area is associated with the horizontal shear of the basic circular flow. The bands of the second and the third mode have not been observed in real storms. Dynamical behavior as well as the energetics of a band are discussed for each mode.
There exists practically no instability in the outer region of the storm for any kind of spiral band. It is speculated that a band which grows in an inner area and propagates outward, i.e., the band of the first mode mentioned above, may become a neutral spiral while moving toward the outer region. Some of the outer spiral bands observed in real tropical cyclones may be interpreted as this kind of internal gravity-inertia waves.