Vertical Structure of Barotropic Isolated Vortex in a Rotating Tank

This is an Amazing picture showing the vertical structure of an isolated columnar vortex in a rotating tank. I've discussed the related mechanisms in our recent NSC report. In this blog, I want to address the possibility to analysis the flow structure by Scaling Analysis to estimate the scale of the local flow structure.

There're several regions of interests, they include:

1. The upper free surface at the vortex center (SD)
   This flow is due to the surface depression of the vortex. Owing to the deformation of fluid surface, the fluid velocity in the vicinity of the vortex center naturally has the vertical downward component . (secondary downward flow)
   
2. The lower solid boundary flow at the vortex center (SU)
   This secendary flow arises from the viscous boundary effect at the tank bottom. Owing to the main stream (a circulation), there exists a radial presure gradient thus steers the flow cyclonically inward to the center. Then, the inward flows are thus emerged to upward until the encountering with the downward flow. (secondary upward flow)
   
3. The internal boundary of the upward secondary flow and the downward surface flow. (IB)
   

By using the boundary layer analysis at the bottom and at the free surface with a vortex distribution (can use the Gaussian vortex distribution) to estimate the resulted characteristic flow velocities.