Vorticity of Aircraft Trailing Vortices

[Danis]

I've recently been studying aircraft trailing vortices and have been reading various papers regarding vortices. However, my aerodynamics is very rusty, I've been confused about the vorticity of these vortices.

In Fundamentals of Aerodynamics (Anderson), Ch 3, Vortex flow is shown to be irrotational everywhere except when r = 0, which has infinitie voriticity. However, all the vortices that I've come across in various papers have a particular (non-zero) vorticity, eg a Gaussian profile for the Lamb-Oseen vortex.

Could someone please help me with this.

Cheers.

 

[minger]

What I think you're referring to are solutions to stream functions and things of that nature. By definition, vorticity is simply:
$$\omega = \vec{\nabla} \times \vec{V}$$
When we think of flows, we can think of them of a summation of translational and vortical components. Vortices will certainly have both components as they can be thought of as spinning eddys, which translate with the mean flow.

 

[dtango]

I've recently been studying aircraft trailing vortices and have been reading various papers regarding vortices. However, my aerodynamics is very rusty, I've been confused about the vorticity of these vortices.

In Fundamentals of Aerodynamics (Anderson), Ch 3, Vortex flow is shown to be irrotational everywhere except when r = 0, which has infinitie voriticity. However, all the vortices that I've come across in various papers have a particular (non-zero) vorticity, eg a Gaussian profile for the Lamb-Oseen vortex.

Could someone please help me with this.

Cheers.

What Anderson is referring to is that the streamlines in a vortex flow are irrotational. In other words if we imagine a parcel of fluid flowing around the streamline of a vortex flow the parcel does not itself rotate as it travels around the "circular" path. The streamline itself is a circular path, but the fluid in the streamline is not spinning. An example would be as if the Earth orbited the sun without the Earth spinning about it's own axis.

Saying that the streamline is irrotational means we are assuming inviscid (non-viscous) flows which simplifies things a whole bunch.

Hope that helps!