First principles expressions are given for the parameters governing collisional diffusion and parallel losses of mass, momentum and energy in tokamak scrape-off layer (SOL) plasmas. These dissipative, or damping, coefficients are based on neoclassical perpendicular transport (Pfirsch–Schlüter diffusion) and classical parallel transport (sub-sonic advection and Spitzer–Härm diffusion). When numerical values derived from these expressions are used to compute damping coefficients for the edge-SOL electrostatic (ESEL) turbulence code, simulations correctly reproduce the radial profiles of particle density, n, and electron temperature, Te, as well as statistical distributions and temporal correlations of particle density and flux density measured in Ohmic and L-mode plasmas on the TCV tokamak. Similarly, preliminary calculations agree reasonably well with radial profiles of Te measured in Ohmic and L-mode plasmas on JET, although the particle density e-folding length is over-estimated by a factor of 3; this discrepancy is largely removed by reducing the parallel density gradient length by a factor measuring the poloidal asymmetry (ballooning) of filament displacements. These encouraging results suggest that turbulent SOL transport is driven by interchange motions, caused by unfavourable curvature and strong pressure gradients in the edge region, with the level of turbulence being influenced by neoclassical diffusion and parallel losses in the SOL region. Moreover, the curvature drive offers a viable mechanism for the origin of the B × ∇B-independent part of the parallel SOL flow measured on many tokamaks, including JET and TCV, with ESEL simulation predicting a parallel Mach number of ≈ 0.2 in JET Ohmic and L-mode plasmas, in fair agreement with Mach probe measurements.