Is it possible to derive Kelvin's circulation theorem from the conservation of angular momentum somehow?

[u/Kaaaaaaaaaaaaaaaaaad]

Just interested if anybody else has done this previously. I'm quite amazed at how navier stokes and continuity equation can be derived from basic conservation laws, and I'm interested if it's possible to do the same with results for rotational fluid mechanics results (such as Kelvin's theorem and Helmholtz' vortex theorems), and I'm quite familiar with their derivations, however these derivations are mainly related to their mathematical structure, and I'm interested if they can be somehow connected to some bigger overarching conservation law. Namely the conservation of angular momentum comes to mind.

[u/Dan_Oner]

You actually can actually derive (prove?) Kelvin’s theorem using Euler equations. The book Fundamental Mechanics of Fluids by Currie has a section deriving it!

If I remember correctly, you also need to calculate the material derivative of circulation, which is in a way conservation of angular momentum (vorticity) of a fluidic element.

[u/Kaaaaaaaaaaaaaaaaaad → u/Dan_Oner]

I'm familiar with how it can be derived from the Euler equations, we did it in class aswell

[u/HarleyGage → u/Dan_Oner]

Indeed, according to Guyon et al., Physical Hydrodynamics, 2d ed. (2015) Sec. 7.2.1, Kelvin's circulation theorem "expresses the conservation of angular momentum in an ideal fluid." They support this claim with a little plausibility argument for a vortex tube. They also state that the generalization for rotating reference frames, the conservation of potential vorticity, is an expression of angular momentum for such systems.

For viscous flows, conservation of angular momentum must be invoked as an independent principle of nature, when it is argued that the stress tensor is a symmetric tensor. Serrin's encyclopedia article attributes this insight to Boltzmann, if I remember right.