[cfdmms]

Hi,
I would like to know, how to differentiate the energy containing and inertial subrang eduring energy spectrum analysis (E vs k)? In general cases, if the spectrum not follow the ideal trend (say, slope -5/3 is not identical in the curve), so how to demark these two ranges.

[FMDenaro]

Originally Posted by cfdmms

Hi,
I would like to know, how to differentiate the energy containing and inertial subrang eduring energy spectrum analysis (E vs k)? In general cases, if the spectrum not follow the ideal trend (say, slope -5/3 is not identical in the curve), so how to demark these two ranges.

Sorry but your question is not clear ... the k^-5/3 law is the theoretical slope for the particular case of the intertial range for homogeneous isotropic turbulence, followed by the dissipative range (for real fluids) starting at the Taylor microscale until the Kolmogorov scale.
Complex turbulent flows do not necessarily obey to such scaling.

Please, reformulate your question

[cfdmms]

Originally Posted by FMDenaro

Sorry but your question is not clear ... the k^-5/3 law is the theoretical slope for the particular case of the intertial range for homogeneous isotropic turbulence, followed by the dissipative range (for real fluids) starting at the Taylor microscale until the Kolmogorov scale.
Complex turbulent flows do not necessarily obey to such scaling.

Please, reformulate your question

Sorry for the confusion. I agree with you that in complex turbulent flow cases they dont obey any of these theoretical scaling. So in case of complex fluid flow cases, in energy spectrum analysis, is it possible to separate these eddy lengthscales (energy containing scales, inertial sub range and dissipation range) in terms of wave numbers?

[FMDenaro]

if an inertial range exists, you will see it plotting the spectrum...
for example consider the case of the channel flow: at low y+ (close to the wall) practically you see no straight slope of the energy curve, but approaching higher y+ (towards the center of the channel) the inertial range (at high Re_tau) will be present.

That means that in complex flows you can have only some region where an inertial range exists

[cfdmms]

Originally Posted by FMDenaro

if an inertial range exists, you will see it plotting the spectrum...
for example consider the case of the channel flow: at low y+ (close to the wall) practically you see no straight slope of the energy curve, but approaching higher y+ (towards the center of the channel) the inertial range (at high Re_tau) will be present.

That means that in complex flows you can have only some region where an inertial range exists

Thanks for the reply. But my confusion still remains. Let say if we do LES of a turbulent flow case and also do the energy spectrum. According to LES, filter width should lies within the inertial subrange to resolve the large scale properly. My question is from the spectum analysis how can we identify that our taken filter width (or corresponding cutoff wavenumbers) are within the inertial subrange?
As you mentioned ealier that most of the complex flow paterns not follow the theoritical trend, so according to me it is important to identify the energy containing range (energy contained low wavenumbers). But how? Looking forward to hear from you.

[FMDenaro]

well, if you use LES the task is more complex....

1) for complex flows you need a local filter widht, that means that in the region where a large inertial range exists you can have a quite large widht but in the other regions you need to practically solve all scales. For example in channel flows you solve the near-walls structures in a DNS-like resolution while the LES filter acts mainly in the horizontal plane.

2) the filter is something that alters the slope of the energy spectrum. For example the top-hat filter introduce a transfer function like G(k)=sin(kh)/kh. Therefore the ideal slope k^-5/3 you see in a DNS simulation, is conversely smoothed in LES at the frequencies where G(k) < 1.

3) doing LES the energy spectrum is totally truncated after the filter wavenumbers, therefore you cannot identify from your simulation all the intertial subrange but only the resolved part. Of course, there is no dissipative range

[cfdmms]

Originally Posted by FMDenaro

well, if you use LES the task is more complex....

1) for complex flows you need a local filter widht, that means that in the region where a large inertial range exists you can have a quite large widht but in the other regions you need to practically solve all scales. For example in channel flows you solve the near-walls structures in a DNS-like resolution while the LES filter acts mainly in the horizontal plane.

2) the filter is something that alters the slope of the energy spectrum. For example the top-hat filter introduce a transfer function like G(k)=sin(kh)/kh. Therefore the ideal slope k^-5/3 you see in a DNS simulation, is conversely smoothed in LES at the frequencies where G(k) < 1.

3) doing LES the energy spectrum is totally truncated after the filter wavenumbers, therefore you cannot identify from your simulation all the intertial subrange but only the resolved part. Of course, there is no dissipative range

Thanks for the illustrative answer. Here, I am expressing my opinion regarding this, please correct me if I am wrong. Let say, if we consider a simple fluid flow case like pipe flow, in that case the largest eddy size (L) will be the diameter (d) of the pipe. According to the cascade process, lengthscale L_EI which separate the energy containing eddies (low wavenumbers in E(k) vs k and anisotropic in nature) and small eddies (high wavenumbes and isotropic) that can be taken as 1/6 of L (according to the Kolmogorov hypothesis of local isotropy) and that can be expressed in terms of wavenumbers in E(k) vs k. On the other hand, the rate of energy transfer in the inertial subrange (L_EI> L_inertial > L_DI or k_EI< k_inertial < k_DI) (here, L_EI separates energy containing and inertial subrange and L_DI for inertial and dissipation range) is constant and follow E(K)=C*epsilon^2/3*k^-5/3. So, the rate of energy transfer (epsilon) for given cutoff wavenumbers (or filter width) for LES can be easily measured and that will be roughly equivalent to the rate of energy transfer of lengthscale L_EI to check whether taken filter width lie within the inertial subrange. Looking forward to hear your opinion on that.

[FMDenaro]

Originally Posted by cfdmms

Thanks for the illustrative answer. Here, I am expressing my opinion regarding this, please correct me if I am wrong. Let say, if we consider a simple fluid flow case like pipe flow, in that case the largest eddy size (L) will be the diameter (d) of the pipe. According to the cascade process, lengthscale L_EI which separate the energy containing eddies (low wavenumbers in E(k) vs k and anisotropic in nature) and small eddies (high wavenumbes and isotropic) that can be taken as 1/6 of L (according to the Kolmogorov hypothesis of local isotropy) and that can be expressed in terms of wavenumbers in E(k) vs k. On the other hand, the rate of energy transfer in the inertial subrange (L_EI> L_inertial > L_DI or k_EI< k_inertial < k_DI) (here, L_EI separates energy containing and inertial subrange and L_DI for inertial and dissipation range) is constant and follow E(K)=C*epsilon^2/3*k^-5/3. So, the rate of energy transfer (epsilon) for given cutoff wavenumbers (or filter width) for LES can be easily measured and that will be roughly equivalent to the rate of energy transfer of lengthscale L_EI to check whether taken filter width lie within the inertial subrange. Looking forward to hear your opinion on that.

no, in pipe/channel flows you cannot estimate via the isotropic/homogenous theory...turbulence structures associated to small scales of the motion are not isotropic.
As I wrote before, only far from the walls you can have tendency to the recover of isotropy