Scaling-equivalent rotating flows

Three outstanding rotating disk flows described by an exact solution of the Navier-Stokes equations are revisited in this paper. The purpose is to find out to what extent the corresponding boundary value problems can be mapped on each other by scaling transformations. The three addressed, and seemingly basically different axisymmetric flows are (A) the flow induced by arough rotating disk, (B) the flow induced by a simultaneouslyrotating and radially stretching disk, and (C) the classicalvon Karman swirl. The main results of the paper can be summarized as follows. (i) The continuous set of solutions of the problem (A) corresponding to(lambda=0,eta>0)is scaling-equivalent to the solution of von Karman, (C), (ii) Every given solution of the problem (A) with(lambda>0,eta >= 0)generates by a suitable scaling transformation a unique solution of (B) withc>ccrit=2.3848, (iii) every given solution of the problem (B) with ac>ccritcan generate a continuous set of solutions of the problem (A), (iv) in the stretching dominated subcritical rangec

Automated summary

The paper revisits three outstanding rotating disk flows described by an exact solution of the Navier-Stokes equations, aiming to investigate the mapping relationships between them. It is found that flow (A) is similar to flow (C), and can generate flow (B) through suitable scaling transformations, while flow (B) can generate a continuous set of solutions of flow (A).