Analysis of the turbulent boundary layer on a rotating disk

 An order of magnitude analysis of the equations of motion governing the turbulent boundary layer on a rotating disk was performed in a stationary coordinate system located at the center of the disk. The governing equations in the wall layer were derived. Using the log law for the tangential velocity, a relation between the tangential friction velocity and the Reynolds number was derived. The forms of the three components of mean velocity in the viscous sublayer were derived. Analysis of the radial momentum equation indicated the existence of two velocity scales that are both dependent on the Reynolds number. This is the reason for the lack of inner scaling observed for the mean radial velocity. The far-wall behavior of the mean tangential and vertical velocity was documented. The analysis, along with measurements, indicated that the mean downward vertical velocity induced at the edge of the boundary layer is on the order of 15% of the tangential shear velocity. Received: 5 July 2001/Accepted: 17 October 2001