We revisit a Lindblad master equation for the propagation of photons carrying orbital angular momentum (OAM) through a turbulent atmosphere. This equation is is here independently derived from the stochastic Hamiltonian formulation of paraxial optics, accounts for the Kolmogorov power spectrum of turbulence, and relies on an exact ensemble average over refractive index fluctuations. We show that, in contrast to previous representations, our present formulation admits efficient numerical solutions on suitably truncated Hilbert spaces, what we exploit in a study of the crosstalk of a single twisted photon propagating through the atmosphere.