@Mr. Bernhard, Thanks for your reply. I did not understand one point. You say that the accuracy of the higher order scheme is so high that the flow instability cannot evolve. It would be great if you could explain this a little more.

I understood your point regarding the lower order scheme. Thanks again.

Bernhard's explanation is partially true for flow past bluff bodies. Our experience with Kuwahara's third order scheme taught us that the upwinding was killing the physical instabilities, as well as, numerical instabilities. Instead if you use simple CD2 scheme you will see Karman vortex street - by a lower order method!! So these order of method business is waste of time.  There are other flow instability parameters, which are the true determinant of vortex shedding.

However, when we later moved to compact schemes (which are known for their near-spectral resolution and dispersion relation preservation properties) the flow exhibited vortex shedding. The fact is that in computing one needs neutrally stable method. As the bluff body flows are characterized by the presence of strong adverse pressure gradient, any minute numerical disturbances act as trigger. Thus, there are NO so-called higher order methods which does not exhibit vortex shedding. It is a myth.

For your help, I am posting the following references:

1) Dynamical system approach to instability of flow past a circular cylinder - Tapan K. Sengupta, Neelu Singh and V. K. Suman, J. Fluid Mechanics, vol. 656, pp 82-115 (2010)

2) Enstrophy-based proper orthogonal decomposition for reduced-order modeling of flow a past cylinder - T. K. Sengupta, S. I. Haider, Parvathi M. K. and Pallavi G., Physical Review E, vol. 91(4), 043303 (2015)

and the text-book:

"High Accuracy Computing Methods: Fluid Flows and Wave Phenomena" (Cambridge Univ. Press, USA, July, 2013) by Tapan K. Sengupta

Feel free to contact, should you have any further queries. Good luck to your research activities.

@Mr. Tapan K. Sengupta, Thank you for your reply sir. I will definitely go through the references and get back in case of any queries. Thank you once again.

Triggering an instability is a numerical issue but is also depending on the formulation you are using. By definition of time-average field, using URANS you can not have in your solution some fequencies.

On the other hand, using DNS or LES, you should take care both on the accuracy order and on the type of discretization. Indeed you should minimize (or eliminate) the numerical dissipation but, at the same time, you must have a stable solution that means once generated the instability at some frequency it must not amplificate

It is not easy to answer you case. There are several factors.

Usually, the vortex shedding is one of self-induced mechanisms.

For example, if you only have simple inlet/outlet w/o  with constant fluxes.

If you introduce the initial disturbance at 3%, but strictly set the inflow at constant velocity.

Vertices will start shedding and keep doing so without needing to add bc disturbances.

Though, some self-induced mechanisms may be slightly damped after time.

1st Point:

When you try to use the periodic bcs. You refeed the disturbance frequency , which in this case your shedding frequency, back at the front. Thus the arrival of this disturbance will change your flow structure. This behavior of excitation will vary depending on the phase of arrival ( you domain lenght/vs strouhal wavelenght) of your fed-back stream. So you have to be really careful. Physics of flow past single cylinder is not the same as the flow through an array of cylinders.

2nd Point.

Tapan is correct about the numerical scheme. There is no such thing as too much accuracy.

It could however, be that, when the grid is not symmetric at your sysmetric plan, low-order may approximate the solution differently and this mismatchs in the momentum balance generate the disturbance themselves , which ultimately set off the self-induced mechanism. This onset, may not even need the initial disturbance at all.  Thus when upgrade the scheme to higher-order, this mismatched is smaller and could be totally damped by the viscous term.  Also, HO upwind scheme could further damp the disturbance as well.

RANS is not a good strategy to solve the proble. Better will be DNS. But well.

Select one smooth solution, maybe steady, and introduce a random perturbation

with certain magnitude (a porcentage of the quantity). That will start the unsteady moving solution.

Could not agree more with Andres. This was the gist of my previous answer where I said that how the problem should be viewed as a problem of scientific computing mimicking natural route. RANS is an absolute "no-no" for such problems. Unfortunately managers want colourful pictures and over-eager engineers provide the same. 

Ideally, one must obtain an equilibrium solution and then study its stability and/or receptivity to different classes of omnipresent background disturbances. Our cited references will tell interested people how it is done computationally.

One should remember that for given (steady or unsteady) boundary conditions the equations of Navier Stokes can have different unsteady solutions, which we could call vortex shedding modes. Hence even a perfect simulation can have results that does critically depend on initial conditions.In the thesis of Anna Mueller (PhD thesis, University Twente and Von Karman Institute for Fluid Dynamics: http://doc.utwente.nl/79375/1/thesis_A_Mueller.pdf) the flow around a square rod is described, which does display two stable wake modes for angles of attack between 23 and 45 degree. The first mode is the periodic vortex shedding mode (Von Karman). This vortex shedding mode corresponds to a whistling sound. The second mode is a silent mode. The turbulent wake does not whistle. One can switch the flow from one to the other mode  to the other by upstream respectively downstream perturbation. URans nor LES calculations did not capture the silent wake mode. While LES results did quite well describe the vortex shedding mode. The results of the URans model was quite disappointing. This is because there occurs some subtle flow separation and re-attachment effects, which are not described by this model.

Hence one should be careful in giving a general answer. Problems can be related to the numerical model or to the actual physics of the flow considered.

URANS is not a model ..it is a formulation that has a specific set of equations in which the resolved variables have a well-specific meaning: time-averaged.

LES also is a specific formulation wherein the variables have a specific meaning: filtered

we should not be disappointed by the fact we decide to use URANS that intrinsically cannot described time-fluctuations in the solution. This is simply a wrong choice in the formulation we used, not a fail in URANS

Cannot agree more than what Filippo stated! This is often taught often in management schools!!