Nonlinear dissipative spherical Alfven waves in solar coronal holes

The weakly nonlinear dynamics of linearly polarized, spherical Alfven waves in coronal holes is investigated. An evolutionary equation, combining the effects of spherical stratification, nonlinear steepening and dissipation d ue to shear viscosity is derived. The equation is a spherical analog of the scalar Cohen-Kulsrud-Burgers equation. Three main stages of the wave evolu tion are distinguished: geometrical amplification, wave breaking and enhanc ed dissipation. The wave dissipation is dramatically increased by the nonli near transfer of energy to smaller scales. The scenario of the nonlinear di ssipation is practically independent of viscosity. The dissipation rate is stronger for highest amplitudes, and depends weakly on the wave period and the temperature of the atmosphere. Waves with periods less than 300 s and i nitial amplitudes about 2-3 % of the Alfven speed at the base of the corona are subject to the nonlinear steepening and dissipation in less than 10 so lar radii. For the Alfven waves with amplitudes less than 25 km s(-1) at th e base of the corona, the maximum amplitude of up to 200 km s(-1) is reache d at several solar radii. The nonlinear distortion of the wave shape is acc ompanied by the generation of longitudinal motions and density perturbation s.