I will soon conduct some experiments on compound channel in unsteady flow case. The flow velocity will be measured using acoustic Doppler velocity. I'd like to have your thoughts about what I'm planning to do to measure velocity in specific moments of the hydrograph. In other terms, I want to avoid the classic and time consuming method (yet efficient) of running the same hydrograph many times (up to 200 runs sometimes) and to average. Here is what I thought:

  1. Since the ADV measures the instantaneous velocity in a point, I'd measure only one time and, instead of running the hydrograph many times, I'll use Fourier transform to the instantaneous velocity measured to extract the mean velocity (I've heard this method is quite used in many other domains). So I was wondering what filter frequency I'd choose to be close to the mean velocity.

  2. Since the ADV measures the instantaneous velocity in a point, I'll measure in about 500 points to estimate the discharge. So I thought that maybe I could detect the point where the measured mean velocity is the more representative (by studying the data of old flow measures in the channel). Thus I'd only measure in the chosen point (so one measurement per cross section, instead of 500 measurements).

Thank you!


You didn't outline the reason why you don't want to use the time-tested and well-validated approach -- and you even identified it as efficient, which usually means it has a good cost vs. quality balance. And based on your questions, it might be worth revisiting why the classic experimental method runs several hundred cases.

In an unsteady flow, things are often quite chaotic due to turbulence. Small perturbations in conditions can lead to pretty significant changes in the flow. Many of these changes are seemingly random and things like intermittancy or bursting can occur at very irregular intervals.

By making a measurement many, many times and averaging them (ie. ensemble averaging), you eliminate most of those perturbations in your initial and boundary conditions. That means that whatever small changes that lead to chaotic flows will usually all average out, and you are left with a "true" representation of the flow based on the expected values of the initial and boundary conditions.

By trying to bypass that, you are introducing a possible source of uncertainty into your results. Let's take your example of measuring just once. It is possible that when you take your measurement, an intermittent vortex is shed somewhere upstream of where you are measuring and that passes through your measurement point. You may have gotten unlucky and that is the only time that vortex has ever or will ever appear, but you happened to measure it. So now your only data signal says a vortex will always be there. But, if you measured 200 times, your data would say that the vortex is unlikely and the results could be different.

Similarly, you are interested in the mean velocity from a time series. That means if you only take a single measurement, it had better be a long (in time) one. How long? Well, it depends on all the possible frequencies of fluctuations in your flow. If you are measuring a river, you might need to measure for a year to account for all of the seasonal variations. If you are measuring a supersonic jet in crossflow, you might only need to measure for a millisecond. You need to make sure your time series is long enough to resolve every possible frequency you want.

So be careful... you might just end up making a lot more work for yourself by trying to bypass the traditional techniques.

To answer your specific question... the mean of a signal is always the component of the FFT with zero frequency. No frequency implies mean. But again, be very careful that your data isn't taken when there is a slow rise or slow decrease of a low frequency trend. You need a long (theoretically infinite, but always truncated in practice) dataset in order to find the true mean.

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  • $\begingroup$ I've qualified the classical method as 'efficient' just based on the literature (it's the method the most used). I agree with you that suggesting that measurement in a single point would represent the cross sectional mean velocity is not very reasonable, especially in my case (compound channel unsteady flow) where the secondary flows are very likely to occur. I'd thought I'd study many old data measurements to study if that point changes a lot along the channel in other cases but I think I'd just give up the idea. I might, as you said, end up with much more work. $\endgroup$ – Yassine Jun 16 '18 at 9:14
  • $\begingroup$ I must admit I don't have much idea about using DFT to extract the mean velocity (the reason why I'm asking) to respond. I've just read in the literature that it may be used, by filtering the noise using a frequency much more less than the one of bursting turbulence (they didn't really detailed). I'm still looking this up (I know that it's used in aerodynamics too, if you have an other sources I'll be thankful). I'll try to bridge the gap between your comment and what I'm reading and I'll answer for your remarks about the DFT. $\endgroup$ – Yassine Jun 16 '18 at 9:15

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