On kinetic theory viscosity in a rotating gas

The subject of angular momentum transport is important in theories concerning accretion disks. The αmodel of Shakura and Sunyaev1) assumes outward transportation of angular momentum due to some viscous force. This viscosity is believed to originate from turbulence, because the molecular viscosity is far too small in this case. Because the viscosity formula for turbulence is not well known, generally accepted practices have relied on the formula for molecular viscosity, with the viscosity coefficient assumed to be far larger than that for actual molecular viscosity.1) In the present paper we investigate the molecular viscosity formula, which can be unanbiguously defined, applicable to a rotating gas. The viscosity formula for shear flow is well known. The shear stress is proportional to the rate of strain. For a shear flow represented by u = (0, U(x)), the x-y component of the shear stress is given by