Dear Deewakar Sharma.
I apologize to others, but the answers were not to the point.
If you looks at basic book on mechanical of turbulence (Tennekes & Lumley; The first couse in turbulence), you will see that already in the introduction does not define the turbulence, but simply characterized. The basic characteristics of turbulence are irregularity, diffusivity, large Reynolds numbers, three-dimensional vorticity fluctuactions and dissipation. And is not defined the same as the turbulence is a flow as a laminar flow (same laws: continuity, NS and energy)!
However in the same book is shown mainly in item 3.3 (Vorticity dynamics), for having dissipation, mixing and diffusivity fluctuations vorticy requires a three-dimensional flow.
What explains the sudden increase in the rate of dissipation and mixing (or diffusivity), is the stretching of the vortices. If two orthogonal vortices undergo a stretch and if these two vortices apply the energy equation on them, we see that the decay rate is always positive, ie a highly dissipative flow.
On the other hand, two-dimensional flow, do not have the same possibility, getting the dissipation rate of molecular diffusion directly linked to the movement of large structures, and not as small dissipative structures (see Obounov-Kolmogorov theory).
This is due to the random character of turbulent fluctuations.
The random nature of the turbulent processes, and therefore its three-dimensionality, is clearly expressed by the emergence of third-order velocity correlations in the derivation of the turbulent shear stresses, which express the process as the Reynolds stresses are conservatively transmitted from one region of the flow to another. For details see Antunes do Carmo (2012).
Antunes do Carmo J.S., 2012. Book “Advanced Fluid Dynamics” - chapter 10 “Turbulent Boundary Layer Models: Theory and Applications”, pp. 205-238. Hyoung Woo Oh (Ed), InTech - Open Access Publisher. ISBN 978-953-51-0270-0 (http://www.intechopen.com/books/advanced-fluid-dynamics) [or ResearchGate].
i suggest that you have a look on chapter 10 of the book "turbulence, an introduction for scientists and engineers", written by P.A. Davidson, Oxford university press: the title of Chapter 10 is " two dimensional turbulence". The beginning of this chapter can be seen on the web through google books at the link : http://books.google.fr/books?id=rkOmKzujZB4C&lpg=PP1&hl=fr&pg=PA569#v=onepage&q&f=false
pages 569 and 570 are a very good answer to your question.
best regards
hubert
The eddies which consist of small scale as well as large scale. To capture these eddies and related effect, the need of 3D CFD. If you related material (Books on Tubulence), provide me your mail id.
A simple way to analyze this to think that the flow is subjected to different conditions of pressure and temperature for each variation of the position of this flow. Changing turn and therefore parameters such as velocity and density, indicates rotational direction changes, under the conditions stated, "are not necessarily circular, and unlikely to be flat."
The best conditions for a 2D planar flow, tidy and would have to be laminar.
Dear Deewakar Sharma.
I apologize to others, but the answers were not to the point.
If you looks at basic book on mechanical of turbulence (Tennekes & Lumley; The first couse in turbulence), you will see that already in the introduction does not define the turbulence, but simply characterized. The basic characteristics of turbulence are irregularity, diffusivity, large Reynolds numbers, three-dimensional vorticity fluctuactions and dissipation. And is not defined the same as the turbulence is a flow as a laminar flow (same laws: continuity, NS and energy)!
However in the same book is shown mainly in item 3.3 (Vorticity dynamics), for having dissipation, mixing and diffusivity fluctuations vorticy requires a three-dimensional flow.
What explains the sudden increase in the rate of dissipation and mixing (or diffusivity), is the stretching of the vortices. If two orthogonal vortices undergo a stretch and if these two vortices apply the energy equation on them, we see that the decay rate is always positive, ie a highly dissipative flow.
On the other hand, two-dimensional flow, do not have the same possibility, getting the dissipation rate of molecular diffusion directly linked to the movement of large structures, and not as small dissipative structures (see Obounov-Kolmogorov theory).
I totally agree with what was said by Rogerio.
In addition just to underline some details to the explanation above stated, one could easily compare the expression of Helmholtz equation in 2D an 3D incompressible ( for instance ) flows.
In 2D flows the stretching term ( omega ° grad ) v ( production of vorticity due to velocity gradient ) vanishes, thus vorticity is directly related to viscous dissipation.
In 3D flows the stretching term in Helmholtz equation does not vanishes and velocity field gradients could stretch and tilt vortex tubes giving vorticity production in the range of the energy containing eddies ( large scales of the velocity field ) .
Regards
Dear Andrea.
Thank you for the help. I'm afraid to place equations in texts by personal traumas, because when I started studying turbulence (thirty years!) I stumbled upon the book Hinze, and due to its approach, my study had delayed more than contributed.
After hearing in the classroom of a great name in the mathematical modeling of turbulence: theory Obounov-Kolmogorov was a simplicity irritating and always it worked, I always try to simplicity.
Dear Taimur take great care when you post comment like that ...
Look at this link:
"http://orderinchoas.wordpress.com/2013/03/03/the-great-leonardo-da-vinci/"
you were talking about the work of "Leonardo Da Vinci" .
Regards,
Andrea
By definition random fluctuations of properties cannot be limited in space ot time.Thats why they are random!
Some think that turbulent flow is always 3D. Some others think that we can define 2D turbulent flows. A great difference is that 2D turbulent flows have an inverse energetic cascade from small scales toward large scales...
Hi,
we must differenciate the types of flow. In neutrally stratified flows we have full 3D character of the turbulence. Please have a look at
http://iopscience.iop.org/1402-4896/2013/T155/014001
where ideal turbulence is derived from the Euler equations, i.e. from the case of vanishing viscosity.
The situation is quite different in stratified and convective flows. Namely stratified flows allow for two-dimensionalisation of the large-scale eddies and reduction of dissipation. I recommend the book
http://books.google.de/books/about/Marine_Turbulence.html?hl=de&id=HVqbdXI29i0C&redir_esc=y
At least the Table of Contents should be readable. You also may buy it from Amazon or Cambridge U. Press. ...
Cheers,
Helmut
Helmut's answer is correct in the sense that stratified and convective flows are different as they allow for two-dimensionalisation of the large-scale eddies. The complete sentence would be that despite this fact, there is an evidence that the small scales are still 3D - in order to allow for the vortex stretching as the great answers mentioned before.
Alex is allright in my view: At smaller scales turbulence always becomes fully 3D -- independent on the structure of larger-scale motions which become also unstable and look like turbulence.
But I have a problem with vortex stretching. It goes as follows. The classical literature on turbulence mentions this phenomenon as a major mechanism within turbulence dynamics. But authors who insist in vortex stretching fail to derive the major universal constants.
My understanding of turbulence is different, see e.g.
http://iopscience.iop.org/1402-4896/2013/T155/014001
It starts from Euler rather than from Navier-Stokes. It neither needs nor one can identify vortex stretching in these equations because there vortices are treated as particles which interact by collisions and kinda solid-state contact like in the devil's gear. But it gives easily universal constants of turbulence like van Karman's and Kolmogorov's constant with anstonishing accuracy, and the free decay and the logarithmic boundary layer, all that without any phenomenological parameter, with geometry and Fokker-Planck statistics only, and without vortex stretching.
I think that vortex stretching is bound to Navier-Stokes and when fricition completely ceases also vortex stretching needs to vanish. Because friction is eventually the lever connecting "to-be-stretched' vortices with large-scale forces? If you look at an ensemble of vortex dipoles in a frictionless medium then the vorticity balance becomes highly intransparent and may even drive you crazy (if you stare long enough at it). I did possibly circumvent this state by concentrating exclusively at energy and vorticity balances of vortex-dipole ensembles. Do vortex dipoles as particle ensemble make the big dot? Maybe a never ending story which drove alredy so many of us crazy and we are only the next ones? However, somehow it's fun ...
Dear Taimur.
If it was so easy to define turbulence as you placed above one already would exist! Read the article "Hypothesis on deterministic turbulence" Yury S. Kachanov (European Journal of Mechanics B / Fluids 40 (2013) 30-33) and you will see that even today there is no clear definition of it.
Chaos theory is based on pre-defined equations with a known number of degrees of freedom, when trying to pass this setting to turbulence that comes the problem, and the problem is not fully closed.
Hinze and Schichting in their monumental books give the answer. No matter what kind is the main flow at a point, the agitations of flow in the three dimensions at that point always exist and produce the 3-D turbulence.
Vortex stretching is one of the characteristics of turbulence. It does not occur in 2D flow. You can read the book: Turbulent Flows by S. B. Pope
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