Dissipation measurements

Please see recent question below.  Does anybody have any comments?

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The question that I was asking is about determing the rate of turbulent energy dissipation. This basically involves measuring the turbulence spectrum using an adv (vector) in the range 1 to 50 Hz (or higher). One hopes to find what is called the 'inertial subrange' where E varies as k to the power -5/3 where k is wave number. In this region the slope of E against k^-5/3 gives the energy dissipation rate. With a single adv one actually measures power against frequency and converting to wave number involves a transformation from freq to k. One way to do that is to asumme Talyors hypotheis of 'frozen turbulence' ie the eddies simply move past the sensor with the mean velocity of the water. Some experiments [] I did clearly indicate that gives much too high a dissipation. I believe a better way is to use two, or even three, ADV's so that one can proeprly assess the spatial correlation. I just wondered if you had information on measurements using this technique with Nortek Vectors.

Here is a comment from Dr. Alexander Sukhodolov
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Dear Atle,

Nice to hear from you.  " />'>  I have a short comment []

The determination of the inertial subrange requires not only validation of -5/3 in the spectra but also the relationship Sv(f; k) = Sw(f; k) = ¾ Su(f; k) should be satisfied which means that the turbulence structures in this frequency (wave number) range are approximately spherical and turbulence respectively isotropic. Although using the conversion of spatial correlation function into wave number spectra is viewed as a superior procedure to the “frozen turbulence” assumption, on the practice the method of multipoint measurements requires very fine grid of measuring points that may be too laborious in comparison with gains it gives. Moreover either method gives only mean estimates for the dissipation rates and actual (instantaneous) values can differ of the order of magnitude (the important aspect discussed by Kolmogorov, see for example in Monin’s and Yaglom’s book). For some illustration of the comparison for spectra estimated from velocity time series and spatial correlation measured with ADVs in the natural environment I refer here to the recent paper Rhoads B., Sukhodolov A. Spatial and temporal structure of shear layer turbulence at a stream confluence. Water Resour. Res. V.40, 2004. (Figure 11).
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