The Question can be Formally presented as follows;
How is the Numerical Model (CFD, Navier Stokes) of fluid dynamics for Vortexes at in it's limits?
At this Publication from 2013 at page 48 is said;
If the free surface is bent at the at the dimple, the complexity and the velocity gradient in the air core is growing fast. At this stage the actual limit is reached that numerical simulations can provide nowadays.
and continued at page 49;
An even more sophisticated step would be an adequate simulation of the air entrainment itself, which is still not possible.
QUESTION; Why it's still not possible?
There is many "exact solutions of NS-equations" for Vortexes; Ie. Burgers Vortex and Lamb-Oseen vortex
Basically Vortex has a clear construction, which can mainly be expressed mathematically very simply way. Ie Rankine Vortex An example of this construction is picture below;
If you look the German-wiki from the "Lamb-Oseen vortex" you find this picture, I modified it to show the interes of my Question (green line).
I am interested about there true shape of this peak. How the numerical model's works at this peak compared to experiments. I think here lies the problem. It's clear that most of the Vortexes aren't like "Lamb-Oseen", but I doubt if they are abslutely like the "Rankine" either. So it's something like the "Burger". When i think the current calculation power, it sound not reasonable that the problem lies just on complexity, as there is even exact solutions available.
Few aspects;
- Energy dissipation rate predicted by the "Lamb-Oseen" is too big, compared to reality.
- Rankine Vortex has an extra pressure gradient in the Water, directed inwards, that prevents evolution of the rigid-body flow to the irrotational state. The counter force of this, might be an extra pressure gradient directed outwards the rigid-body, and this might be the cause to such an stable air core, as told here; How deep can a whirlpool descend?
- There is really interesting experiments made which are able to visualize this phenomenon very nice.
- I am thinking the area marked with red line &question mark in the first picture?
