Torsional wave dispersion and dissipation in solar tornados

{We shed light on the propagation and dissipation of torsional Alfv\'en waves and fast magnetoacoustic torsional waves in solar tornadoes. The efficiency of the plasma viscosity and magnetic diffusivity in the context of energy transfer is highlighted in various layers of the solar atmosphere inline with the increase and decrease of their phase speeds due to the nature of tornadoes.} {Solar tornadoes created by equilibrium magnetic twist and plasma rotation are studied analytically by implementing the resistive magnetohydrodynamic theory in cylindrical geometry. The dispersion relations are obtained for the dependence of the frequency and phases speeds of torsional oscillations on the wave number. The dispersion relations obtained by the second order thin flux tube approximation enables considering damping effects connected with magnetic diffusivity and plasma viscosity. The damping is not a stand alone scenario, as they are influenced by the magnetic twist and plasma rotation in addition to plasma-β conditions.} {The efficiency of damping due to magnetic diffusivity is enhanced by stronger equilibrium twisted magnetic fields. The torsional fast magnetoacoustic wave is more subject to dispersion in the zero-plasma-β limit in the presence of diffusive and viscous effects. The dispersion due to magnetic diffusivity is enhanced by the plasma-β. The presence of plasma viscosity enhances the efficiency of the plasma-β regarding dispersion effects. The damping of torsional fast magnetoacoustic waves in solar tornadoes due to magnetic duffusivity is proportional to the equilibrium magnetic twist for both photospheric and coronal conditions. The efficiency of damping is more pronounced in photospheric conditions. The damping due to magnetic diffusivity is significantly enhanced in the presence of plasma viscosity. The viscosity has a stronger damping effect in lower plasma-β conditions. In photospheric conditions, the equilibrium magnetic twist is less effective in comparison to coronal conditions when both magnetic diffusivity and plasma viscosity are present. As damping is affected by resistance, various modes dissipate subject to atmospheric conditions providing a sustainable heating mechanism in the solar atmosphere.} {The model provides a theoretical basis for development of MHD seismology of solar tornadoes.}