Turbulent flow on a rotating disk

The dissipation theorem is applied to describe fully developed turbulent flow on a rotating disk. A complicated coordinate transformation is proposed to solve the problem. The similarity exponent m becomes a parameter of the problem and can vary gradually with the Reynolds number. This solution may span the entire range from laminar to fully developed turbulent flow, although not accounting for all features observed in the transition region. The profiles of the various quantities are required to be well behaved, and this requirement is used to determine m at different Reynolds numbers. The results are in harmony with the literature and show how different geometries can be treated in a unified manner, with differences arising naturally from those geometric differences but with utilization of similar forms for the decay of the dissipation.