Formation and scaling of primary and secondary vortices

Vortex formation is a limiting process.

When a plate is accelerated from rest, a primary vortex is formed close to the tip of the plate.

This vortex grows up to a limit when it pinches-off from the plate tip.

After the separation of the primary vortex, secondary vortices are generated.

These secondary vortices are similar to each other but smaller in size and lower in strength than the leading vortex.

We experimentally study the growth of vortices around a rotating rectangular plate in a quiescent fluid to analyze the differences between primary and secondary vortices.

The Reynolds number based on the maximum rotational velocity of the plate varies from 2790 to 11170.

The growth of the primary vortex stops when the plate has travelled 31°, for all Re.

At this angular position, the dimensionless strength and maximum vorticity reach their limit values.

The size of the primary vortex remains approximately constant during the formation process.

The circulation of the primary vortex increases solely due to the increase of the vorticity in the vortex core.

The strength and size of secondary vortices are not influenced by the Reynolds number.

The size of secondary vortices is only slightly smaller compared to the primary vortex.

The strength and the vorticity, scaled with respect to the plate chord and rotational speed, are ¼ smaller than the values measured for the primary vortex.

The strength of secondary vortices is lower due to a lower level of vorticity entrained in their core.

These results allow us to give a physical explanation about the difference between primary and secondary vortices.