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We study the propagation, reflection, and turbulent dissipation of Alfvenwaves in coronal holes and the solar wind. We start with the Heinemann-Olbertequations, which describe non-compressive magnetohydrodynamic fluctuations inan inhomogeneous medium with a background flow parallel to the backgroundmagnetic field. Following the approach of Dmitruk et al, we model the nonlinearterms in these equations using a simple phenomenology for the cascade anddissipation of wave energy, and assume that there is much more energy in wavespropagating away from the Sun than waves propagating towards the Sun. We thensolve the equations analytically for waves with periods of hours and longer toobtain expressions for the wave amplitudes and turbulent heating rate as afunction of heliocentric distance. We also develop a second approximate modelthat includes waves with periods of roughly one minute to one hour, whichundergo less reflection than the longer-period waves, and compare our models toobservations. Our models generalize the phenomenological model of Dmitruk et alby accounting for the solar wind velocity, so that the turbulent heating ratecan be evaluated from the coronal base out past the Alfven critical point -that is, throughout the region in which most of the heating and accelerationoccurs. The simple analytical expressions that we obtain can be used toincorporate Alfven-wave reflection and turbulent heating into fluid models ofthe solar wind.

Alfven Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: an Analytical Treatment