DNS is a the best way to solve the dynamics equations since all turbulent scales are resolved adequately. A compete description of the fluid flow can nicely be obtained but unfortunately just for a limited range of Reynolds number.
We often touch on forcing schemes through shaking our system in order to maintain a given energy level and avoid dissipation. Forcing can be accomplished using several techniques, such as Eswaran and Pope's stochastic scheme (1988), or by holding the energy constant in the 2 lowest wavenumber modes. An other idea is to force through a variable negative viscosity in a wavenumber range that fixes the kinetic energy.
I would like to know whether adding these terms in the motion equation do not change the flow physics. Thank you!
Of course the flow physics change. The decay of energy does not remain natural. Any forcing term is based on assumptions that 'model' the expected flow behaviour below a specified cut-off scale. By definition, this brings in an element of approximation depending on the accuracy of the assumptions made. The only true DNS simulation would be one which resolves the flow right down to the Kolmogorov scales
The fact is that turbulence by the forcing term(s) is "weak" turbulence. Many DNS simulations indicate that it is generated by the nonlinear terms in the NSE. Moreover, mathematical analysis shows that turbulence based on the forcing term is finite dimensional, while it is infinite dimensional from the convective terms (with sufficient Re) of NSE
Of course adding a forcing term, either initially or continuously, in DNS is a mathematical action, typically used in CFD studies of homogeneous isotropic turbulence (HIT). To my opinion his is a valid idea in studying the physics of turbulence. Of course the conditions of HIT never perfectly occur. But also exact initial conditions are never met. So in principle only statistics can be simulated with some accuracy. Applying any initial condition is applying a forcing as well!
Taking a step back from N-S, and looking at this question from a different perspective, if you read Kolmogorov (1962) you will see he includes a term for the effect of large scale forcing in his log-normal model. Recent work has focused intensely on how this affects the cascade. Hence, forcing has an impact on the cascade and, thus, momentum.
Following CJ Keylock, one can e.g. see this in atmospheric application in Nastrom+Gage(1985) and more recently (1990's on) papers by Lindborg, where the up- or down-scale transfer of energy (or variance, or stress) is considered.
Abdallah, you ask a lot of questions. But they are good ones, I just can't help answering.
The hope has always been that if you force at large scales (small wavenumbers) then after a few cascades of the energy to smaller scales it won't know/care/be-dependent-on where the energy came from. So the small scales (inertial range and dissipation range) should be independent of the forcing. Unfortunately, this is mostly hope. The idea of a cascade from one scale to the next is a good first-order approximation. But it is only that. Energy can, and does, occasionally go straight from the forcing scales to any other scale (bypassing the cascade). So you 'see' the forcing to some extent at all scales. All forcing actually disrupts the cascade a bit (leading to less dissipation).
I stir the turbulence in a completely physical way in my simulations.
There is no forcing.
Then I don't have to worry about unphysical affects appearing in the turbulence.
The price is you need a more complex solver that can handle wall BCs.
Fourier spectral codes will not work ...
This paper is open access and describes it all.
J. B. Perot, Determination of the Decay Exponent in Mechanically Stirred Isotropic Turbulence, Advances in Physics, 1, 022104, 2011. http://dx.doi.org/10.1063/1.3582815
Dear Abdallah
The very simple answer is that this force can be sent to the pressure term. This term only transfer the energy from the large scale to the small scales. Therefore the turbulence physics does not change.
Prof. A.A. Ranjbar
Dear Abdullah,
Thanks for stirring such an interesting discussion. There are various opinions here and many different aspects of the problem have been highlighted. It is evident that many different approaches are possible to TAILOR the simulation to given conditions. However, I believe that any customisation, or forcing, would limit the applicability to relevant flows only and would not provide a generalised solution. Any mathematical treatment of the governing equations obviously introduces a physical force or source in the problem which would actually not exist in the flow physics. Therefore, forcing only serves to address the limitations of our simulation and should be understood as such.
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