I think that Sec.2.1 in this paper can answer your question

Article Hussain, F.: On the identification of a vortex. JFM 285, 69-94

If the air is to move along a curved path, there must be a centripetal acceleration toward the center of the curve: Newton's second law says that acceleration must be caused by some force. If viscosity is small, that force must be the pressure force -- there are no other candidates. So the pressure gradient must be high on the outside of the curve, low on the inside to apply an inward force. (quoted from agate_)

As Mr. Ingo Riess mentioned in his answer (quoted from agate_ on reddit), I understand that the reason a vortex core is considered to be a region of local pressure minima is because the pressure gradient is able to provide the required centripetal force for the fluid to rotate.

What I would like to know is weather anti cyclones can be considered as a vortex in true sense, as they have a mass of fluid rotating about a center (please correct me if I am wrong), but an anticyclone has a high pressure region at its core. Also what provides the required centripetal force for the anticyclone.

I think that Sec.2.1 in this paper can answer your question

Article Hussain, F.: On the identification of a vortex. JFM 285, 69-94

There are different types of “vortices”. First define it mathematically and then discuss the solution of the pressure. Some rotational motions are called for instance solid body rotation of the velocity is increasing with the radius. Some are with a viscous core and decreasing velocity beyond this radius. So first is the velocity field and then the pressure (or vice versa)

I totally agree, and in practice the real vortex structures is a region with such mixed beahaviors, the velocity being somehow proportional at 1/r only up to a certain lenght scale R where the real viscosity is able, even if small, to produce a relevant stress effect similar to a rigid body rotation proportional to r.

Just a note on the distinction between the identification of a vortex in a field at a certain time and the identification of coherent vortex that requires a correlation in time to be meangful.

Hi Fillipo! Are you implying that coherent structures (even for incompressible flows) are not necessarily vortical structures? I agree with Kritikesh that coherent-structure identification tools were developed from Pressure Poisson Equation or Pressure Hessian equation to track minima of pressure. However, in weather system, one needs to understand the implication of geostrophic assumption. Such an assumption, makes variations of pressure in atmosphere completely different from lab-scale flows. One can read the beautiful description in the book by Tritton (for Kritikesh!).

Hi! Well, I just would highlight the fact that "vortex structure" and "coherence" are somehow weak (in the sense of not well defined) definitions and are subject to issues in practical use. The paper I posted above also highlighted that, starting from the standard definition of Lamb (also detailed in the book of Chorin) of a vortex structure as a tube (having arbitrary initial line) envelop of vorticity field, this identification can fail to detect a vortex but can be still considered "coherent".

Years ago we had some research about that but for several reasons we did not continue to explore such field. Also the lambda-2 criterion has some issue to detect vortex in confined flows. However, I have not followed the recent literature about this task, maybe improvements were reached.

Thanks Filippo! I do not think the situation has improved at all. We are proposing two physical criteria for tracking disturbances instead, to avoid the semantics of what constitute a vortex. That way, one can trace from the onset stage to fully developed stage of turbulence for incompressible flows.

You are also absolutely right about lambda-2 criterion, where unsteady and viscous terms are dropped to capture "coherent structures" - an act of self-fulfilling prophesy. This type of practice must have a "law" stated in management studies! I will be damned, if there aren't any!!

Have a great day!

I'm afraid there's nothing "coherent" in some of the "coherent structures" except our own imagination :)

Absolutely right Alex! That in essence summarizes the answers to Kritikesh's original query. Coherent structures and pressure minima are not synonymous.

Filippo sir, I am trying to understand the various criteria for 'vortex identification'. You mentioned that lambda2 criteria has some issues detecting vortex in confined flows. Would you mind shedding some light as to what these might be? If possible with a link to an article explaining the same in detail.

The flow over a wall is characterized by a wide range of characteristic lenght scales for the vortical structures. If you try to detect such structures using exactly the value lambda2=0 you will see that the criterion will detect a confusing pattern.

Just some improvements can be obtained by introducing some averaging and setting a negative value for lambda 2.

These articles show our experience with this criterion:

Article Analysis of 3-D backward-facing step incompressible flows vi...

Article High order filtering for control volumes simulation

yes, "coherence" is somehow an hystorical denomination that has never reached a rigorous definition shared in the community...something similar is the adopted denomination "eddy".

After years of exposure to the vortex identification issue I came to the very personal conclusion that, probably, it is not a well posed question as, in practice, we don't actually know well what we really want to identify. We gave it a name, but we are confused on what we actually want to see on the math/physics ground. This is intended in the sense of having several possible identification techniques, but we still have to decide which one of them is that "vortex" we actually want to see.

Filippo Maria Denaro and Paolo Lampitella: Agree completely. The missing rigour and general excitement of turbulence research community has bypassed the issue of what and how coherent structure in turbulence to be characterized. Surely, some competent scientists will seize the initiative and develop a fully developed theory. Till such time, we should try to distinguish between vorticity and vortex!

I can only say that years ago we start from the simple definition of vortical tube, exactly as defined rigorously in the Chorin's textbook. Well, since from a laminar confined flow the detected patterns were quite confused...

not all vortices have a low-pressure core (for example, an anticyclone has a

high-pressure core, with the Coriolis force balancing the radial pressure gradient) (See Epps AIAA paper, 2017, Review of Vortex Identification Methods)

For vortex identification, our recent new paper give more comments. Please refer to the paper: Third generation of vortex identification methods: Omega and Liutex/Rortex based systems, Article Third generation of vortex identification methods: Omega and...

@Jianming Liu can you please indicate what are the first two generations of vortex identification methods? It would also help tremendously to distinguish all the three methods, identifying similarities and dissimilarities among these.

Tapan K. Sengupta Hi Professor. Helmholtz proposed the concepts of vorticity tube/filament in 1858, which can be categorized as the first generation of vortex identification methods.During the last three decades, a lot of vortex identification methods, including Q ,Delta, lambda_ci , and lambda 2 criteria, have been proposed to overcome the problems associated with vorticity-based methods. Most of these criteria are based on Cauchy-Stokes decomposition and/or eigenvalues of the velocity gradient tensor and can be considered as the second generation of vortex identification methods. The detail is given in the paper Article Third generation of vortex identification methods: Omega and...

Of course, such a classification may be controversial, but the article show it may be reasonable.