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 Anders Jönson August 16, 2000 03:20

Definition of Coherent Structure?

Hi,

Is there a definition the term coherent structure? Can anyone explain what it is and give an example of it?

Regards Anders

 ZhengTong Xie August 16, 2000 06:49

Re: Definition of Coherent Structure?

Hi,

Is it not easy to define conherent sturcture? Howerver, there are some examples: votex street behind a cylinder, big votex in free shear layer, and maybe hair-pin votex in boundary layer flow.

Zhengtong

 Klaus August 16, 2000 07:36

Re: Definition of Coherent Structure?

Hi,

I think a good mechanism to find coherent parts is to build a correlation (auto - cross) to find similarities between the information you want to investigate. As long as they show contrubition to your correlation as long they are related together as long they are coherent.

 Patrick Godon August 16, 2000 08:54

Re: Definition of Coherent Structure?

A coherent structure is a structure present in the flow for a relatively long time, it is not just a transient phenomenon. The example that comes to my mind is the vortex.

For example in a turbulent flow, say two dimensional for simplicity, there are many structures that will look like vortices but only for a very short period of time. They will have a rotational velocity and will look kind of circular, but if they do not last more than a (few) dynamical time(s), then they are transient, non-coherent and are defined just as Eddies.

However, if you have an 'Eddy' that stays there for quite a while and does not seem to disappear, then it is actually already a vortex rather than an Eddy and it is not transient any more. These structures can last a viscous time scale and more, depending on the conditions and these are coherent structures.

THe weather pattern on earth look (from a satelite) pretty much chaotic, except for some regular wind patterns (jet stream in the atmosphere, El nino in the sea etc..). When a Huricane (cyclone, typhoon) forms, it is actually a coherent vortex sustained by (upwards) convective current of hot air (because of the earth rotation - Coriolis forces etc.. - the hot air also rotates as it goes towards the center of huricane and up).

Another example is the Great Red Spot in the atmosphere of the Giant Planet Jupiter. There are many small little and transient Eddies there, but there is one big large huricane-kind of vortex which has been observed for almost 300 years, it is the Great Red Spot. There are also other smaller coherent vortices but this one is the best known.

Any patterns that is not transient and that is sustained in the flow for a (relatively) long time is a coherent structure.

Patrick Godon

 Kalyan August 16, 2000 13:39

Re: Definition of Coherent Structure?

In an approximate sense, a coherent structure is a region of flow where the two point correlations do not have the same behavior as in fully developed turbulence.

i.e. If x is a point in a coherent structure of size R, the correlation <u(x)*u(x+r)>, where r < R, does not decay with increasing "r" as in fully developed turbulence (i.e. scaling laws of fully developed turbulence). If the flow is statistically stationary, the correlation can be Eulerian. If the coherent structures are moving, the flow is non-stationary and one needs to compute a Lagrangian correlation.

The main difficulty in detecting a coherent structure is in computing the correlations. For more detailed discussions, look in books by Monin and Yaglom and/or papers by Fazle Hussain on the subject.

 Mayank Tyagi August 16, 2000 18:11

Re: Definition of Coherent Structure?

Reference:

"Eddy structure identification" J.P. Bonnet (Eds)

It contains a lot of information about coherent structures and their identification in flow fields

regards

Mayank

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