Hi,

I have a small confusion regarding using the terms vortex and eddy. My doubt is 'what is vortex and eddy?' 'where are this terms appropriate to be used?' 'what is the difference between them?'

may be this is silly question but if anyone can help I would thanks him in advance.

Ravi

More appropriately, "thank her/him in advance"

Ok, I also agree with you.

These terms are used loosely, without exact definition. However, a vortex is a region of concentrated vorticity, while an eddy is a closed streamline region. Often these coincide, but consider, for example, the steady flow with uniform vorticity past an obstacle on a flat plate, with zero velocity at the plate far upstream. Then, there is a separation region (= eddy) upstream of the obstacle but no vortex. I cannot invent at the moment a clear example of a vortex without surrounding eddy, but you may try to imagine a very weak vortex in a strong stream.

Again, the terms are close and not exact.

I am not very much clear about your example, if you can write some more details it will be very helpful. I would like to add few more questions related to the topic.

Vorticity values can give some idea about, how much fluid element has been stretched? (which contribute to generate stress in the fluid element). What more can be understood by the vorticity values? similarly, what can be interpreted if we say eddies are formed? what physical interpretation does this words can give in describing the fluid motion? Usually, this words are quite common in use while describing the result obtained by CFD.

Well, regions of closed streamlines can exist even if vorticity is constant. My example was that of an inviscid flow with vorticity constant throughout the flow field. Far upstream it is a shear flow, u=y+1,v=0, 2D case considered (Did I write u=0 at the flat plate at infinity? Sorry, that would do, too, but it is better to take u=y+1). Flow domain is y>0 and x**2+y**2>1 (that is the flow past a semi-circular cylinder mounted on a flat plate). In this flow there are closed streamline regions in front and behind the cylinder. I believe, Joukovski considered this flow, but that was long ago and in Russian only, I am afraid. The problem is, it may be difficult for you to see intuitively how this flow looks like, this needs certain experience. If your would have it, you would not ask the question, though.

>Vorticity values can give some idea about, how much fluid element has been stretched?

Directly, no. Vorticity is a measure of fluid rotation, not stretching. Vorticity equals twice the rotation speed of a fluid element. However, if the vorticity field is known then the velocity field can be found quite easily. The advantage of using vorticity when describing fluid motion is that vorticity behaviour is simpler than velocity behaviour. One hardly can understand fluid flows without understanding the vorticity dynamics. This, however, is a large topic and it is usually quite well discussed in standard texts on fluid dynamics. I recommend Batchelor's 'Introduction to fluid dynamics' and/or Lighthill's 'Informal introduction to fluid dynamics' (the titles may be slightly different, English is not my native language).

>what can be interpreted if we say eddies are formed?

Generally, we know how the fluid moves if we know how its particles move. Usually, two particles initially close to each other will move apart, consider velocity field u=y, v=w=0 (shear flow). Particles in the eddy remain in the eddy for a long time. Hill's vortex is an eddy (see Batchelor's book). Separation region in a steady flow is an eddy. Karman vortices behind a body are eddies. Anyway, you need examples. Many can be found in Van Dyke's 'Album of fluid motion'.

Well, today I am going on a trip, and I do not know when I will get access to WWW. Hopefully, what I wrote gives you a start, at least.

Hi,

You can take a look at

Jeong J. & Hussain F (1995) On the identification of a vortex, J. Fluid Mech. vol. 285 pp. 69-94.

Have fun,