Based upon a critical review, the target of this paper is to reshape a theoretical framework under which one may justify if relative slow sediment transport processes, such as soil creep. a turbulent flow or not. Under this theoretical viewpoint, soil creep is treated as a special granular flow whose velocity is always slow, and such a slow and dense granular flow shows significant velocity fluctuation that can be observed in both field measurement and laboratory experiment. For describing slow turbulent, a compatible modified Reynolds number, Re', is proposed with some conjectures. For laminar flow without any significant velocity fluctuation, Re' gives the same value as the conventional Reynolds number, Re', does. However. Re' manage to recognise the slow turbulent granular flow, meanwhile keeps different kinds of flux flow under the same framework of justification. Taking for an example. Re is equal to 500 for a river with 0.5-cm•sec^(-1) flow velocity, 10-cm flow depth, and a water temperature of 20℃ (i.e., ν=0.01 cm^2•secj^(-1) while Re' is equal to 3500 which is in the transitional range close toward the turbulent flow in fluid dynamic literatures. Applying Re' to soil creep having annual speed of 1 mm with an average speed fluctuation about 90% of the annual speed, the diffusion coefficient (i.e., viscosity in such a case) is then about 0.81 mm^2 year^(-1). If the characteristic length (L) is defined as the wavelength of a terracette (about 1.2 meter). then Re' gives '2681', while the conventional Re gives only '1481'. Notice that L is chosen as 1.2 meter, and implies that the constant creeping speed can be realised only over a distance of 1.2 meter, or equivalently we can have constant creeping rate under the measurement duration of 1,200 years.