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Abstract Cyclostrophic rotation in the core region of tropical cyclones (TCs) imprints a distinct signature upon their turbulence structure. Its intensity is characterized by the radius of maximum wind, , and the azimuthal wind velocity at that radius, . The corresponding cyclostrophic Coriolis parameter, /, far exceeds its planetary counterpart, , for all storms; its impact increases with storm intensity. The vortex can be thought of as a system undergoing a superposition of planetary and cyclostrophic rotations represented by the effective Coriolis parameter, . On the vortex periphery, merges with . In the classical Rankine vortex model, the inner region undergoes solid‐body rotation rendering constant. In a more realistic representation, is not constant, and the ensuing cyclostrophic ‐effect sustains vortex Rossby waves. Horizontal turbulence in such a system can be quantified by a two‐dimensional anisotropic spectrum. An alternative description is provided by one‐dimensional, longitudinal, and transverse spectra computed along the radial direction. For rotating turbulence with vortex Rossby waves, the spectra divulge a coexistence of three ranges: Kolmogorov, peristrophic (spectral amplitudes are proportional to ), and zonostrophic (transverse spectrum amplitude is proportional to ). A comprehensive database of TC winds collected by reconnaissance airplanes reveals that with increasing storm intensity, their cyclostrophic turbulence evolves from purely peristrophic to mixed peristrophic‐zonostrophic to predominantly zonostrophic. The latter is akin to the flow regime harboring zonal jets on fast rotating giant planets. The eyewall of TCs is an equivalent of an eastward zonal jet.