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Oliver September 5, 2000 13:51

Vortex flow fields & Nature
Hi All

I need a prepectives on the following Dilemma.

Vortex flow fields in general are dominated by 2 velocity profiles.

1. Swirl Velocity profiles, are well established by a burger or even more simply by a rankine vortex

2. An axial velocity profile, which can either have a wave like or jet like velocity profile depending totally on the criticality of the flow. [Supercritical and Subcritical vortex flow]

My question now is as follows, Why inside the core of a vortex, does the axial velocity exceed or subceed that of the irrotational flow field, Why must it be so?.

Regards Oliver

Vidyadhar Y. Mudkavi September 12, 2000 00:26

Re: Vortex flow fields & Nature
i am confused by your question. could you clarify as to what you mean by axial velocity exceeding (or otherwise) the "irrotational flow field." do you mean why the axial velocity must exceed the swirl velocity?

Oliver September 12, 2000 12:27

Re: Vortex flow fields & Nature
Hi Vidyadhar

In general across a vortex, the swirl velocity profile is in equilibrium with the radial pressure gradient and is well accounted for by Burgers Vortex.

In reality a vortex cannot exist without an axial velocity profile, it must be travelling through space. It travels say with a non-uniform axial velocity profile. Right at the center of the eye of the vortex, the axial velocity either exceeds that of the free stream axial velocity outside the vortex core.

My question is as follows; is it simply because there is a pressure minimum at the center of the vortex that the axial velocity exceeds that of the axial velocity outside the vortex core and why did nature intend on it to be so.

Any insight or perspective would be of great interest to me

Regards oliver

Vidyadhar Y. Mudkavi September 13, 2000 00:25

Re: Vortex flow fields & Nature

if you take a burgers vortex or a rankine vortex, it is indeed possible for them to exist without any axial flow. it is also perfectly ok for them to sustain an axial velocity profile.

however, if you take a rankine vortex (or burgers) and allow the core size to vary along the axis, then continuity suggestst that there must be some axial velocity. often, the perturbation of the core can lead to enhancement of the axial component and a simultaneous decrease in the swirl component. this, of course, follows from simple physical reasoning. often this is related to the vortex bursting which is so visible in natural flows (particularly wing tip vortices in the context of aircraft wakes).

the presence of axial velocity, to begin with, has a lot to do with its generation. if you are talking about such vortices as the hurricane, tornado etc, they are created by natural forces. it is impossible to think of nature to choose a clean burger or rankine vortex without any axial component in it! experimentally achieving such vortical flows without any axial flow can be a daunting task.

i am not sure if i have clarified your doubt further. i do hope so, though.

Oliver September 13, 2000 17:47

Re: Vortex flow fields & Nature
Hi Vidyadhar

First of all thanks for the insight.

1.However a burger vortex is derived from the N.S equations and must always contain an axial velocity profile (uniform axial distribution).

2. A burger or rankine vortex can be produced by a rotating cylinder in a body of fluid and as such are artificial.

3. A vortex goes to great length to preserve the swirl velocity distribution (preferred case), such that there is a pressure minimum at the centre of the vortex, and as such the axial velocity is induced. Why is the case? Why does it not balance the axial velocity profile firstly, then think about the swirl velocity distribution?.

Regards Oliver

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