[lucamirtanini]

Hi all,
I would like to calculate the Taylor microscale. I am reading the Tennekes and Lumley textbook. It seems that it is possible to calculate this Taylor microscale starting from the autocorrelation of the velocity fluctuation, but I am not sure how to do it. Can anyone help me?

[FMDenaro]

Originally Posted by lucamirtanini

Hi all,
I would like to calculate the Taylor microscale. I am reading the Tennekes and Lumley textbook. It seems that it is possible to calculate this Taylor microscale starting from the autocorrelation of the velocity fluctuation, but I am not sure how to do it. Can anyone help me?

You can read Pope to get further infos. A practical technique is to use the fitting of the parabola at the origin.
Have a read also here


https://agupubs.onlinelibrary.wiley....2/2013JA019641

[lucamirtanini]

I did the autocorrelation in the time domain. Then I did the parabolic fitting of the autocorrelation, but the fitting curve is not tangent but secant, as shown in the figure. How can I fix this issue?

[FMDenaro]

The correct procedure is reported in pag 198-199 in the Pope textbook

[lucamirtanini]

Ok. Thank you. If I do the autocorrelation of the time history, the taylor microscale is a space scale or a time scale?

[LuckyTran]

If you get it from the temporal correlation, it's the time-scale. Common practice is convert that to the length scale by invoking Taylor's frozen hypothesis

[FMDenaro]

Originally Posted by lucamirtanini

Ok. Thank you. If I do the autocorrelation of the time history, the taylor microscale is a space scale or a time scale?

Why don't you simply compute from the spatial autocorrelation?

[lucamirtanini]

Originally Posted by FMDenaro

Why don't you simply compute from the spatial autocorrelation?

If I compute the spatial autocorrelation, of data obtained through numerical calculation, I am afraid that the mesh can affect the estimation of the Taylor microscale if the mesh is coarse. I will try it btw

[FMDenaro]

Originally Posted by lucamirtanini

If I compute the spatial autocorrelation, of data obtained through numerical calculation, I am afraid that the mesh can affect the estimation of the Taylor microscale if the mesh is coarse. I will try it btw

Of course, I assume you are performing a DNS. Otherwise in any other formulation the computation of the Taylor microscale has no meaning.

[lucamirtanini]

I am running a LES. My mesh is coarse, but my time step is short. So, maybe, the time taylor scal can be reliable, isn't it?

[LuckyTran]

Originally Posted by lucamirtanini

I am running a LES. My mesh is coarse, but my time step is short. So, maybe, the time taylor scal can be reliable, isn't it?

It doesn't matter how arbitrarily small your time-step is, the temporal resolution doesn't improve the length scales that is being filtered/resolved by the LES. An LES that resolves down to the Taylor microscales is practically a DNS.

Algorithmically you can still compute the temporal or spatial autocorrelation and do the extrapolation. It's a good mechanical learning exercise if that's what you are trying to do.

Another example is if you did URANS with a super-fine grid. You can follow the steps to calculate the autocorrelation. But you know it is URANS and doesn't have any turbulence in it. It doesn't matter how small your time-step is or how fine your grid is, your velocity needs to be the right kind of velocity in order to get a meaningful autocorrelation in the first place.

[promise89]

Originally Posted by lucamirtanini

I did the autocorrelation in the time domain. Then I did the parabolic fitting of the autocorrelation, but the fitting curve is not tangent but secant, as shown in the figure. How can I fix this issue?

How you find microscale from the autocorrelation graph. I have series so Which procedure I need to follow to apply parabolic fitting?